{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0001","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"61ec4b5e9492bfe0524eb5dc501e358ff9eaf99740b990f82bc54f736a944d06","family_id":"qf-statistics-observation-mean","seed":202610067001,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"0\",\"1\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[0]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"0/1","explanation":"Sum all 1 observations with their multiplicities and divide by that positive count, obtaining 0/1. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0002","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eed7f88dfab7ab573912646875f183aee244458ee0b72aa262316d5cfb036e64","family_id":"qf-statistics-observation-mean","seed":202610067002,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-3\",\"1\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[-3, -3, -3]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-3/1","explanation":"Sum all 3 observations with their multiplicities and divide by that positive count, obtaining -3/1. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0003","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b170076dc4a6ee2b0bb48317ade6667a1a870016863722ada26677499609c16","family_id":"qf-statistics-observation-mean","seed":202610067003,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-4\",\"1\"],[\"1\",\"1\"],[\"8\",\"1\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[-4, 1, 8]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"5/3","explanation":"Sum all 3 observations with their multiplicities and divide by that positive count, obtaining 5/3. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0004","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d1595e798a9613a3ce9286533d1a4564f6e997e2beeb17002be45d66e3aa3fd3","family_id":"qf-statistics-observation-mean","seed":202610067004,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-2\",\"1\"],[\"5\",\"1\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[-2, -2, 5, 5]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"3/2","explanation":"Sum all 4 observations with their multiplicities and divide by that positive count, obtaining 3/2. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0005","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2444e757a2c6847cc32cc27da053a804aaa7b51896698434f46bcaabd9bc3430","family_id":"qf-statistics-observation-mean","seed":202610067005,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-7\",\"2\"],[\"2\",\"1\"],[\"8\",\"2\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[-7, -7, 2, 8, 8]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"4/5","explanation":"Sum all 5 observations with their multiplicities and divide by that positive count, obtaining 4/5. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0006","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c51fe3ca52c2ab8ed58528c0d342ba1cd4c783eb7e23304a592d11db46ab9f2b","family_id":"qf-statistics-observation-mean","seed":202610067006,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-7\",\"3\"],[\"1\",\"1\"],[\"8\",\"2\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[8, 8, 1, -7, -7, -7]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-2/3","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -2/3. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0007","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4518ab81b5ce16046d3167e787b97887af00a6cc997903deb14c8b52c5bab8ed","family_id":"qf-statistics-observation-mean","seed":202610067007,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-8\",\"1\"],[\"-1\",\"2\"],[\"9\",\"3\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[9, 9, 9, -1, -1, -8]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"17/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 17/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0008","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"16968816e091ab48e00d48f522478ccbc09b7ab52c19e1b805ade3353d613020","family_id":"qf-statistics-observation-mean","seed":202610067008,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-9\",\"2\"],[\"0\",\"3\"],[\"10\",\"1\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[10, 0, 0, 0, -9, -9]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-4/3","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -4/3. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0009","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5fe391ad19645081f92309b9b02544e16806809cb3a7b9be026fda7b9d49722f","family_id":"qf-statistics-observation-mean","seed":202610067009,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-10\",\"3\"],[\"1\",\"1\"],[\"11\",\"2\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[11, 11, 1, -10, -10, -10]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-7/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -7/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0010","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1cc1da676b18ce4d49546dcb61a4550c6c590662c173dbe82ac155876b289f79","family_id":"qf-statistics-observation-mean","seed":202610067010,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-11\",\"1\"],[\"-1\",\"2\"],[\"12\",\"3\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[12, 12, 12, -1, -1, -11]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"23/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 23/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0011","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c5fff789333ced65cc9430fefb670d203c98bf9dd011becd817fd97eac10822","family_id":"qf-statistics-observation-mean","seed":202610067011,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-12\",\"2\"],[\"0\",\"3\"],[\"13\",\"1\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[13, 0, 0, 0, -12, -12]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-11/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -11/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0012","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e9d568f6c508a51b14000c20fb4b2f1cfbeda14ad3f453ef0cb438feea3136b","family_id":"qf-statistics-observation-mean","seed":202610067012,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-13\",\"3\"],[\"1\",\"1\"],[\"14\",\"2\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[14, 14, 1, -13, -13, -13]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-5/3","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -5/3. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0013","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5e25febd46300955a22bcfc127fecb749ab389ad5d694d6b6ab6570d53567522","family_id":"qf-statistics-observation-mean","seed":202610067013,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-14\",\"1\"],[\"-1\",\"2\"],[\"15\",\"3\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[15, 15, 15, -1, -1, -14]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"29/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 29/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0014","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fdf6f5d72a7699a4c21b8db6c20dfa31d5d0830854be1f02b88189662c256002","family_id":"qf-statistics-observation-mean","seed":202610067014,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-15\",\"2\"],[\"0\",\"3\"],[\"16\",\"1\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[16, 0, 0, 0, -15, -15]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-7/3","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -7/3. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0015","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce5fa07a50fc5ee465846b5cf519b9156cf08b0fa2b4a21f4e9676994f487cc3","family_id":"qf-statistics-observation-mean","seed":202610067015,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-16\",\"3\"],[\"1\",\"1\"],[\"17\",\"2\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[17, 17, 1, -16, -16, -16]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-13/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -13/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0016","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"23e14c79000e53a61f54950a0632e39c1ee48db2b415dd0cb745ff0113828383","family_id":"qf-statistics-observation-mean","seed":202610067016,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-17\",\"1\"],[\"-1\",\"2\"],[\"18\",\"3\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[18, 18, 18, -1, -1, -17]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"35/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 35/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0017","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a9ec287c817289b7a361743d97001d3fb3193b7fc9f3a4ae085d63ad9957df8a","family_id":"qf-statistics-observation-mean","seed":202610067017,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-18\",\"2\"],[\"0\",\"3\"],[\"19\",\"1\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[19, 0, 0, 0, -18, -18]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-17/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -17/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0018","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c582a8f17d9f455f358d81ce5a1be89fb37d98090ce6225c8570549ea5c865b","family_id":"qf-statistics-observation-mean","seed":202610067018,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-19\",\"3\"],[\"1\",\"1\"],[\"20\",\"2\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[20, 20, 1, -19, -19, -19]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-8/3","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -8/3. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0019","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"450fa301ebcec184b93f871a635626a7a9fb7008c54e7eb559f4c9a492f03360","family_id":"qf-statistics-observation-mean","seed":202610067019,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-20\",\"1\"],[\"-1\",\"2\"],[\"21\",\"3\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[21, 21, 21, -1, -1, -20]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"41/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 41/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0020","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7a4e09a972f7ee1cbd1ffcb04d61c9a7773c6f369c249047af8a4f42cb17f692","family_id":"qf-statistics-observation-mean","seed":202610067020,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-21\",\"2\"],[\"0\",\"3\"],[\"22\",\"1\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[22, 0, 0, 0, -21, -21]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-10/3","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -10/3. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0021","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1fa35d51458d015b4bf4ba4ff781a1108413da3dd5e8467da29f2bc92ad40e57","family_id":"qf-statistics-observation-mean","seed":202610067021,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-22\",\"3\"],[\"1\",\"1\"],[\"23\",\"2\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[23, 23, 1, -22, -22, -22]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-19/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -19/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0022","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc3901b0d2bc7857b5da085a7a1424582ec6f814e309e9aa7cfffa91e5ea609c","family_id":"qf-statistics-observation-mean","seed":202610067022,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-23\",\"1\"],[\"-1\",\"2\"],[\"24\",\"3\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[24, 24, 24, -1, -1, -23]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"47/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 47/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0023","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b22581ec37d28ad8b8261b99ab112260b4fe912c4596e606d4edb31414a265d9","family_id":"qf-statistics-observation-mean","seed":202610067023,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-24\",\"2\"],[\"0\",\"3\"],[\"25\",\"1\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[25, 0, 0, 0, -24, -24]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-23/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -23/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0024","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ef65a5df03633fcaa912f1805f025de0d31e209e82b10e6f836c221e6914c1e3","family_id":"qf-statistics-observation-mean","seed":202610067024,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-25\",\"3\"],[\"1\",\"1\"],[\"26\",\"2\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[26, 26, 1, -25, -25, -25]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-11/3","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining -11/3. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0025","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5804b8e761330b5e0cbbe5703fb9cd5c401db6d38fd393be65c0111a56bfa71f","family_id":"qf-statistics-observation-mean","seed":202610067025,"semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-26\",\"1\"],[\"-1\",\"2\"],[\"27\",\"3\"]],\"operation\":\"observation_mean\"}"},"fields":{"title":"Arithmetic Mean Retaining Multiplicities","stem":"The nonempty observation list is D=[27, 27, 27, -1, -1, -26]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"53/6","explanation":"Sum all 6 observations with their multiplicities and divide by that positive count, obtaining 53/6. Do not average a deduplicated set or infer a population probability law."},"skills":["Arithmetic Mean Retaining Multiplicities"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0026","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"faf2cda3a7f0f49e8f9318b2fd260d9e22e37107e88e4fe81192449e9a551050","family_id":"qf-statistics-observation-median","seed":202610067026,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"0\",\"1\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[0]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"0/1","explanation":"The sorted list retaining repetitions is [0]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0027","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"398db2694a5541e8bac387e4f6fce617dd6580fca590a1242960c5231b9b19de","family_id":"qf-statistics-observation-median","seed":202610067027,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-3\",\"1\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[-3, -3, -3]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-3/1","explanation":"The sorted list retaining repetitions is [-3, -3, -3]. Apply the stated odd/even convention to obtain -3/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0028","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1f7dfadec46244907f880c16ec69dd71d0f50169ead90c40f7f5b6710b1a1edb","family_id":"qf-statistics-observation-median","seed":202610067028,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-4\",\"1\"],[\"1\",\"1\"],[\"8\",\"1\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[-4, 1, 8]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"1/1","explanation":"The sorted list retaining repetitions is [-4, 1, 8]. Apply the stated odd/even convention to obtain 1/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0029","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"66db53e4392438685d718cf666c405b085e0f93596c77125921ffe0749c901a0","family_id":"qf-statistics-observation-median","seed":202610067029,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-2\",\"1\"],[\"5\",\"1\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[-2, -2, 5, 5]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"3/2","explanation":"The sorted list retaining repetitions is [-2, -2, 5, 5]. Apply the stated odd/even convention to obtain 3/2; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0030","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5e3d4de7bb55591e717fc7f7e60b64c24b201bb5fae8f3f622d0605e59cccffa","family_id":"qf-statistics-observation-median","seed":202610067030,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-7\",\"2\"],[\"2\",\"1\"],[\"8\",\"2\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[-7, -7, 2, 8, 8]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"2/1","explanation":"The sorted list retaining repetitions is [-7, -7, 2, 8, 8]. Apply the stated odd/even convention to obtain 2/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0031","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8d037b3c637cca2a13d687847160a5a2bef0a09dfa8a6d9049147e51b6ed8a21","family_id":"qf-statistics-observation-median","seed":202610067031,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-7\",\"3\"],[\"1\",\"1\"],[\"8\",\"2\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[8, 8, 1, -7, -7, -7]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-3/1","explanation":"The sorted list retaining repetitions is [-7, -7, -7, 1, 8, 8]. Apply the stated odd/even convention to obtain -3/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0032","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2296522a70353245cedf83c218230113e415c29d7d1a49f0d6d6d6f959c9141d","family_id":"qf-statistics-observation-median","seed":202610067032,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-8\",\"1\"],[\"-1\",\"2\"],[\"9\",\"3\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[9, 9, 9, -1, -1, -8]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"4/1","explanation":"The sorted list retaining repetitions is [-8, -1, -1, 9, 9, 9]. Apply the stated odd/even convention to obtain 4/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0033","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"92dde9b895b02ca0ee4f562a2f5cfd9bc9ab821d2ba5461b4f79179a4abd0a5b","family_id":"qf-statistics-observation-median","seed":202610067033,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-9\",\"2\"],[\"0\",\"3\"],[\"10\",\"1\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[10, 0, 0, 0, -9, -9]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"0/1","explanation":"The sorted list retaining repetitions is [-9, -9, 0, 0, 0, 10]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0034","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4d083c22fe766d7a6688af31f2b0a663e9056d4ea1b1a2cda796d9172af582f6","family_id":"qf-statistics-observation-median","seed":202610067034,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-10\",\"3\"],[\"1\",\"1\"],[\"11\",\"2\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[11, 11, 1, -10, -10, -10]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-9/2","explanation":"The sorted list retaining repetitions is [-10, -10, -10, 1, 11, 11]. Apply the stated odd/even convention to obtain -9/2; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0035","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e32abae811de9940821103fdd4f5254920c1c5cf0a2ce37234f29352d92d3c57","family_id":"qf-statistics-observation-median","seed":202610067035,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-11\",\"1\"],[\"-1\",\"2\"],[\"12\",\"3\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[12, 12, 12, -1, -1, -11]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"11/2","explanation":"The sorted list retaining repetitions is [-11, -1, -1, 12, 12, 12]. Apply the stated odd/even convention to obtain 11/2; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0036","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e9b9c2b84b50f5e60227b5bd7e025c916fda668fa83b4d789b5d106602ee7e09","family_id":"qf-statistics-observation-median","seed":202610067036,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-12\",\"2\"],[\"0\",\"3\"],[\"13\",\"1\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[13, 0, 0, 0, -12, -12]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"0/1","explanation":"The sorted list retaining repetitions is [-12, -12, 0, 0, 0, 13]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0037","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bc2f7b6f4d2b6a72ecebbfe8805bbfcd227bfce059930360cbde2583598e84fe","family_id":"qf-statistics-observation-median","seed":202610067037,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-13\",\"3\"],[\"1\",\"1\"],[\"14\",\"2\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[14, 14, 1, -13, -13, -13]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-6/1","explanation":"The sorted list retaining repetitions is [-13, -13, -13, 1, 14, 14]. Apply the stated odd/even convention to obtain -6/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0038","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"57c120bd754fce9a3b159b3ebd2a65d6c897871494b1f8cd0bb59579657acbfc","family_id":"qf-statistics-observation-median","seed":202610067038,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-14\",\"1\"],[\"-1\",\"2\"],[\"15\",\"3\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[15, 15, 15, -1, -1, -14]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"7/1","explanation":"The sorted list retaining repetitions is [-14, -1, -1, 15, 15, 15]. Apply the stated odd/even convention to obtain 7/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0039","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fcc661b778c390910eb7b8cdd67020f7ada07e68c545d380002f13b0e0bec2c7","family_id":"qf-statistics-observation-median","seed":202610067039,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-15\",\"2\"],[\"0\",\"3\"],[\"16\",\"1\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[16, 0, 0, 0, -15, -15]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"0/1","explanation":"The sorted list retaining repetitions is [-15, -15, 0, 0, 0, 16]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0040","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f85e90096fd6ff7adeb398cb5642fcd0b53eec09b5d44e1bf5c975bd0533b7af","family_id":"qf-statistics-observation-median","seed":202610067040,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-16\",\"3\"],[\"1\",\"1\"],[\"17\",\"2\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[17, 17, 1, -16, -16, -16]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-15/2","explanation":"The sorted list retaining repetitions is [-16, -16, -16, 1, 17, 17]. Apply the stated odd/even convention to obtain -15/2; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0041","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4233a41b749d12254315d56b2983b6cd623495939bc2c5c0cf801aa9cf49629e","family_id":"qf-statistics-observation-median","seed":202610067041,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-17\",\"1\"],[\"-1\",\"2\"],[\"18\",\"3\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[18, 18, 18, -1, -1, -17]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"17/2","explanation":"The sorted list retaining repetitions is [-17, -1, -1, 18, 18, 18]. Apply the stated odd/even convention to obtain 17/2; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0042","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee47bb8e94cf76527f6ceb4ae19f41f937c38ad5a110dfd4b77e0abaf31a0edf","family_id":"qf-statistics-observation-median","seed":202610067042,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-18\",\"2\"],[\"0\",\"3\"],[\"19\",\"1\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[19, 0, 0, 0, -18, -18]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"0/1","explanation":"The sorted list retaining repetitions is [-18, -18, 0, 0, 0, 19]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0043","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c5a9adfc9ac582f9956ce61212a08a71a2fda6a1650c634d5da33c22179be62a","family_id":"qf-statistics-observation-median","seed":202610067043,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-19\",\"3\"],[\"1\",\"1\"],[\"20\",\"2\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[20, 20, 1, -19, -19, -19]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-9/1","explanation":"The sorted list retaining repetitions is [-19, -19, -19, 1, 20, 20]. Apply the stated odd/even convention to obtain -9/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0044","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5cc5f53e9f1ff158f35eb581a6a2015c747febc358d497d4d50c587933cf4afb","family_id":"qf-statistics-observation-median","seed":202610067044,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-20\",\"1\"],[\"-1\",\"2\"],[\"21\",\"3\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[21, 21, 21, -1, -1, -20]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"10/1","explanation":"The sorted list retaining repetitions is [-20, -1, -1, 21, 21, 21]. Apply the stated odd/even convention to obtain 10/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0045","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"81d3451a4206e02f0da91717612b12e0084cbaeaaae9bc7e0b46540fad9c2ce1","family_id":"qf-statistics-observation-median","seed":202610067045,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-21\",\"2\"],[\"0\",\"3\"],[\"22\",\"1\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[22, 0, 0, 0, -21, -21]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"0/1","explanation":"The sorted list retaining repetitions is [-21, -21, 0, 0, 0, 22]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0046","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d76af9c2ff766875677e6bc8fd2e05c2e9336ed71be641cb4c35645e9b17e79d","family_id":"qf-statistics-observation-median","seed":202610067046,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-22\",\"3\"],[\"1\",\"1\"],[\"23\",\"2\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[23, 23, 1, -22, -22, -22]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-21/2","explanation":"The sorted list retaining repetitions is [-22, -22, -22, 1, 23, 23]. Apply the stated odd/even convention to obtain -21/2; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0047","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cbdf226487b985bb964c349ed91dcd0548426546f4854f01ac83b9ea007427be","family_id":"qf-statistics-observation-median","seed":202610067047,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-23\",\"1\"],[\"-1\",\"2\"],[\"24\",\"3\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[24, 24, 24, -1, -1, -23]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"23/2","explanation":"The sorted list retaining repetitions is [-23, -1, -1, 24, 24, 24]. Apply the stated odd/even convention to obtain 23/2; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0048","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd78209b0c5075382d530967bc0b4439ce197666dc3246d29b2f703892186f71","family_id":"qf-statistics-observation-median","seed":202610067048,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-24\",\"2\"],[\"0\",\"3\"],[\"25\",\"1\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[25, 0, 0, 0, -24, -24]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"0/1","explanation":"The sorted list retaining repetitions is [-24, -24, 0, 0, 0, 25]. Apply the stated odd/even convention to obtain 0/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0049","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4be07b62d69df02c0ac3fe1d40c46ad696d21284b72ba6b560b5576f162fa6db","family_id":"qf-statistics-observation-median","seed":202610067049,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-25\",\"3\"],[\"1\",\"1\"],[\"26\",\"2\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[26, 26, 1, -25, -25, -25]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"-12/1","explanation":"The sorted list retaining repetitions is [-25, -25, -25, 1, 26, 26]. Apply the stated odd/even convention to obtain -12/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0050","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"737a4835095ad003df908fcfed853a9e9fa00f70fb9a563d0cbb439c316fb965","family_id":"qf-statistics-observation-median","seed":202610067050,"semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-26\",\"1\"],[\"-1\",\"2\"],[\"27\",\"3\"]],\"operation\":\"observation_median\"}"},"fields":{"title":"Exact Median of an Odd or Even Observation List","stem":"The nonempty observation list is D=[27, 27, 27, -1, -1, -26]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.","answer":{"kind":"expression","value":"13/1","explanation":"The sorted list retaining repetitions is [-26, -1, -1, 27, 27, 27]. Apply the stated odd/even convention to obtain 13/1; the even-length median need not be an observed value."},"skills":["Exact Median of an Odd or Even Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0051","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9588a2f249fd8242421e0b94d40e4edd49feaa94a850d4abb2f17b886160a1ad","family_id":"qf-statistics-observation-range","seed":202610067051,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"0\",\"0\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[0]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"0","explanation":"Subtract the least observation from the greatest to obtain 0. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0052","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d6426109e2d0b64b46e0bdac64442f18c68f6358dc000fdd838f837cd6fba3b8","family_id":"qf-statistics-observation-range","seed":202610067052,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-3\",\"-3\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[-3, -3, -3]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"0","explanation":"Subtract the least observation from the greatest to obtain 0. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0053","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fa3cda242fc7fdbd26f79f6a6265063e5cc113bdaa7d6a9b7ab329060419912c","family_id":"qf-statistics-observation-range","seed":202610067053,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-4\",\"8\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[-4, 1, 8]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"12","explanation":"Subtract the least observation from the greatest to obtain 12. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0054","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aebbad9e49e5711be875c15762d85df0bf88d99f6f6a72429bc71ad7bdc39330","family_id":"qf-statistics-observation-range","seed":202610067054,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-2\",\"5\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[-2, -2, 5, 5]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"7","explanation":"Subtract the least observation from the greatest to obtain 7. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0055","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0bb65069eeeabccde12e770ed9699b5496e132bbc0ff69b78784335c8dd0a1e1","family_id":"qf-statistics-observation-range","seed":202610067055,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-7\",\"8\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[-7, -7, 2, 8, 8]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"15","explanation":"Subtract the least observation from the greatest to obtain 15. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0056","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fe82c24bdaadbe1040289bd0209293efa5c9cc40610d1fd6b7ac259d55642611","family_id":"qf-statistics-observation-range","seed":202610067056,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-8\",\"9\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[9, 9, 9, -1, -1, -8]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"17","explanation":"Subtract the least observation from the greatest to obtain 17. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0057","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5fa4274c2cd0e1dcafe1cf69de7fe59f403387b69f7e10d8c9d77a4da4cafcf0","family_id":"qf-statistics-observation-range","seed":202610067057,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-9\",\"10\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[10, 0, 0, 0, -9, -9]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"19","explanation":"Subtract the least observation from the greatest to obtain 19. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0058","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bd4affa599df5a9fd5db0dbe2f0e48595bd7281e1ca01ee6e49bdbf675df39fd","family_id":"qf-statistics-observation-range","seed":202610067058,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-10\",\"11\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[11, 11, 1, -10, -10, -10]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"21","explanation":"Subtract the least observation from the greatest to obtain 21. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0059","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e1ba9105ee513a0ed8cd935320f43f7e30f5d2a600b5341689bb4831db1c56bb","family_id":"qf-statistics-observation-range","seed":202610067059,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-11\",\"12\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[12, 12, 12, -1, -1, -11]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"23","explanation":"Subtract the least observation from the greatest to obtain 23. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0060","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3b35a637fbed781aa55f0515b5e152e5367a303c0ff5c29ddd6e56e2900ac9ff","family_id":"qf-statistics-observation-range","seed":202610067060,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-12\",\"13\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[13, 0, 0, 0, -12, -12]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"25","explanation":"Subtract the least observation from the greatest to obtain 25. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0061","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c74a21f1e376f741ac6da7c7e87d7766aef7227ff6d549b1efb4a78c3f9e079e","family_id":"qf-statistics-observation-range","seed":202610067061,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-13\",\"14\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[14, 14, 1, -13, -13, -13]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"27","explanation":"Subtract the least observation from the greatest to obtain 27. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0062","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5492ffa75fff47961570079e70d1cbc431f2b795f578dd0ebb550ea8860d1db3","family_id":"qf-statistics-observation-range","seed":202610067062,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-14\",\"15\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[15, 15, 15, -1, -1, -14]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"29","explanation":"Subtract the least observation from the greatest to obtain 29. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0063","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aa1384e5fa3cc0fd7b5868f7e2a6ee6a85a1c30075c80d32a7c90bb57b9166b7","family_id":"qf-statistics-observation-range","seed":202610067063,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-15\",\"16\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[16, 0, 0, 0, -15, -15]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"31","explanation":"Subtract the least observation from the greatest to obtain 31. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0064","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd0d6ad50d18aa05b05030a56f3a5e3db8f301a47f08f90ebfff97be71f3a6b6","family_id":"qf-statistics-observation-range","seed":202610067064,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-16\",\"17\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[17, 17, 1, -16, -16, -16]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"33","explanation":"Subtract the least observation from the greatest to obtain 33. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0065","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3d3e7a28cc57e74a2076737d65cbf214c905b79f466fc3da445a2e39d5b50549","family_id":"qf-statistics-observation-range","seed":202610067065,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-17\",\"18\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[18, 18, 18, -1, -1, -17]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"35","explanation":"Subtract the least observation from the greatest to obtain 35. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0066","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7f08c7cd68129f9c5d46b305657b70297725763a62273b7e2025903fcb3051df","family_id":"qf-statistics-observation-range","seed":202610067066,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-18\",\"19\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[19, 0, 0, 0, -18, -18]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"37","explanation":"Subtract the least observation from the greatest to obtain 37. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0067","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5214e140eca1e773952a0c64f7ff25ebe98e316a9891e432e3d5d3237b9e4e62","family_id":"qf-statistics-observation-range","seed":202610067067,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-19\",\"20\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[20, 20, 1, -19, -19, -19]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"39","explanation":"Subtract the least observation from the greatest to obtain 39. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0068","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8d929b8f52b50ddc3b1342b9e39e8f05cb4c8e4fb22206a9b8e0216b5dd013f1","family_id":"qf-statistics-observation-range","seed":202610067068,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-20\",\"21\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[21, 21, 21, -1, -1, -20]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"41","explanation":"Subtract the least observation from the greatest to obtain 41. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0069","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d7a6faa25c8c75a71bc13ccc4e140c357d1d0f0dfafed0b796bcaec096913ac1","family_id":"qf-statistics-observation-range","seed":202610067069,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-21\",\"22\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[22, 0, 0, 0, -21, -21]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"43","explanation":"Subtract the least observation from the greatest to obtain 43. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0070","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"292fff4c5c0698dc5a8328c05babdb8ab205f52e62e42f0dee38ad2319522352","family_id":"qf-statistics-observation-range","seed":202610067070,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-22\",\"23\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[23, 23, 1, -22, -22, -22]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"45","explanation":"Subtract the least observation from the greatest to obtain 45. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0071","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5a830e4f1f52193039fc9480c29e92ece4f340f5d02e3821ea79b9aa386027fb","family_id":"qf-statistics-observation-range","seed":202610067071,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-23\",\"24\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[24, 24, 24, -1, -1, -23]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"47","explanation":"Subtract the least observation from the greatest to obtain 47. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0072","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"780283e4f13721f471b4585638cc3be69c409e13ec91abda20a5ef182cb20a06","family_id":"qf-statistics-observation-range","seed":202610067072,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-24\",\"25\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[25, 0, 0, 0, -24, -24]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"49","explanation":"Subtract the least observation from the greatest to obtain 49. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0073","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5b4ad1adae8b4fbd55d7df984181674264303944653c8d13ca9b88256be39c61","family_id":"qf-statistics-observation-range","seed":202610067073,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-25\",\"26\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[26, 26, 1, -25, -25, -25]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"51","explanation":"Subtract the least observation from the greatest to obtain 51. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0074","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee55a3325cb98530bc63935ba6ebac0ea3f2ddedb31f278bc59e5a63c5cc6870","family_id":"qf-statistics-observation-range","seed":202610067074,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-26\",\"27\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[27, 27, 27, -1, -1, -26]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"53","explanation":"Subtract the least observation from the greatest to obtain 53. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0075","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6fddbce77bb5c307c264eedccbbca7b18e8ea2db2d38446f999067da593d1796","family_id":"qf-statistics-observation-range","seed":202610067075,"semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-27\",\"28\"],\"operation\":\"observation_range\"}"},"fields":{"title":"Range of an Observation List","stem":"The nonempty observation list is D=[28, 0, 0, 0, -27, -27]. Retain every repetition. Find the range, defined as maximum minus minimum.","answer":{"kind":"short_text","value":"55","explanation":"Subtract the least observation from the greatest to obtain 55. A singleton or constant list has range zero; this is neither variance nor a count of distinct values."},"skills":["Range of an Observation List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0076","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6470cf2411bbc9370167a7a74af944e9001fb5afd968f3c6ff735e9dfb26cbaf","family_id":"qf-statistics-maximal-frequency-set","seed":202610067076,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"0\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[0]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{0}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0077","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"735f52caa9e1560447216785abf29cc264938dd7360d803d4807c27df9720abf","family_id":"qf-statistics-maximal-frequency-set","seed":202610067077,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-3\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[-3, -3, -3]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{-3}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-3}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0078","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"489fe2191e33d682fa21f2c4458c530e65bf821fd337a174442b87bd0b62d8d4","family_id":"qf-statistics-maximal-frequency-set","seed":202610067078,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-4\",\"1\"],[\"1\",\"1\"],[\"8\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[-4, 1, 8]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{-4, 1, 8}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-4, 1, 8}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0079","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eff8e20b2f024df85dcc2e99e0b928d9986a0a5a4a2c445c89485478d07f2042","family_id":"qf-statistics-maximal-frequency-set","seed":202610067079,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-2\",\"1\"],[\"5\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[-2, -2, 5, 5]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{-2, 5}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-2, 5}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0080","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64fdccb00970701402939d7989131457dd586e6a145e5a4df788db68ade75947","family_id":"qf-statistics-maximal-frequency-set","seed":202610067080,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-7\",\"2\"],[\"2\",\"1\"],[\"8\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[-7, -7, 2, 8, 8]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{-7, 8}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-7, 8}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0081","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"272b51675a2bc049fc8faf8e20fcc9471ae384520427da7e3e0e8169db8a3d2a","family_id":"qf-statistics-maximal-frequency-set","seed":202610067081,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-7\",\"3\"],[\"1\",\"1\"],[\"8\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[8, 8, 1, -7, -7, -7]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{-7}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-7}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0082","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9d12440e4fe0af0c59fa319bcf8fd5b1d8162b35a8974efd8af30f301ceb40d4","family_id":"qf-statistics-maximal-frequency-set","seed":202610067082,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-8\",\"1\"],[\"-1\",\"2\"],[\"9\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[9, 9, 9, -1, -1, -8]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{9}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {9}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0083","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2e22cad3d665e4b838667fe5b5eaf48b9c761c3638a925af70c020232c12ef6e","family_id":"qf-statistics-maximal-frequency-set","seed":202610067083,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-9\",\"2\"],[\"0\",\"3\"],[\"10\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[10, 0, 0, 0, -9, -9]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{0}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0084","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ece638b7ccf19b7c83822d2c8e04e05d6841280963a7fa57380bcc80f3a47a06","family_id":"qf-statistics-maximal-frequency-set","seed":202610067084,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-10\",\"3\"],[\"1\",\"1\"],[\"11\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[11, 11, 1, -10, -10, -10]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{-10}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-10}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0085","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cbc58c6f6474aeb06d39150eb5ca4de8f67332d730a163b71d4a0a3a5d4e699c","family_id":"qf-statistics-maximal-frequency-set","seed":202610067085,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-11\",\"1\"],[\"-1\",\"2\"],[\"12\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[12, 12, 12, -1, -1, -11]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{12}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {12}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0086","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f8e1babfb635a60f009b9676409110d4bdda80823871a493eb7bdd5aef22da08","family_id":"qf-statistics-maximal-frequency-set","seed":202610067086,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-12\",\"2\"],[\"0\",\"3\"],[\"13\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[13, 0, 0, 0, -12, -12]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{0}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0087","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2c68c06b386edb2d546e163e58a0e4933bf400aa85eca84ce275d6eb6a386e5d","family_id":"qf-statistics-maximal-frequency-set","seed":202610067087,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-13\",\"3\"],[\"1\",\"1\"],[\"14\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[14, 14, 1, -13, -13, -13]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{-13}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-13}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0088","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"08c4bf5dd5f6d0209416f6cd7192317b8a3c0435183ef6dd822ae8c70d03780e","family_id":"qf-statistics-maximal-frequency-set","seed":202610067088,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-14\",\"1\"],[\"-1\",\"2\"],[\"15\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[15, 15, 15, -1, -1, -14]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{15}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {15}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0089","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2cac2a7664f2b35f0db6c1bd047b2e7623f02a5a57a87ba4edc5858ffc124f00","family_id":"qf-statistics-maximal-frequency-set","seed":202610067089,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-15\",\"2\"],[\"0\",\"3\"],[\"16\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[16, 0, 0, 0, -15, -15]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{0}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0090","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c90221d89fd3092032251c852c8227b4505b16f3e5d19d90fb5e38c015d81984","family_id":"qf-statistics-maximal-frequency-set","seed":202610067090,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-16\",\"3\"],[\"1\",\"1\"],[\"17\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[17, 17, 1, -16, -16, -16]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{-16}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-16}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0091","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8e6476b0a3d80f9b48758a9739cabfb1b51fea842b9973788e778fee7aeecac4","family_id":"qf-statistics-maximal-frequency-set","seed":202610067091,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-17\",\"1\"],[\"-1\",\"2\"],[\"18\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[18, 18, 18, -1, -1, -17]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{18}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {18}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0092","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5ca46eef19f8aebefdae9a691cf2558d7506ac76349af1759e5ed05e0fd922a4","family_id":"qf-statistics-maximal-frequency-set","seed":202610067092,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-18\",\"2\"],[\"0\",\"3\"],[\"19\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[19, 0, 0, 0, -18, -18]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{0}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0093","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6f713da2f8b6b8ed2d402a2bdbb10bec74bf3d1679e798300252e5da510e9255","family_id":"qf-statistics-maximal-frequency-set","seed":202610067093,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-19\",\"3\"],[\"1\",\"1\"],[\"20\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[20, 20, 1, -19, -19, -19]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{-19}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-19}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0094","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"08fe89361ee65b80954815ea24dfcb58670a6e572c354c03157db076921e8cfa","family_id":"qf-statistics-maximal-frequency-set","seed":202610067094,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-20\",\"1\"],[\"-1\",\"2\"],[\"21\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[21, 21, 21, -1, -1, -20]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{21}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {21}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0095","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a5f4d20e9fc4cc9d1b3825320ec880a59744e9ff07819ee5f97712c7fbef5a6d","family_id":"qf-statistics-maximal-frequency-set","seed":202610067095,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-21\",\"2\"],[\"0\",\"3\"],[\"22\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[22, 0, 0, 0, -21, -21]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{0}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0096","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"16f1228f5b2671c54519682f31bd87ffe4ab85308c0be874eaf16e03e47476d1","family_id":"qf-statistics-maximal-frequency-set","seed":202610067096,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-22\",\"3\"],[\"1\",\"1\"],[\"23\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[23, 23, 1, -22, -22, -22]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{-22}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-22}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0097","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"63f061e516938251e07a99f16de625f8d771d2a459b74bb341dd294769e370c3","family_id":"qf-statistics-maximal-frequency-set","seed":202610067097,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-23\",\"1\"],[\"-1\",\"2\"],[\"24\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[24, 24, 24, -1, -1, -23]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{24}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {24}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0098","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"126077e645f80624d2a56a4e30d11593c9f34404e057f829a20317b789f5fb29","family_id":"qf-statistics-maximal-frequency-set","seed":202610067098,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-24\",\"2\"],[\"0\",\"3\"],[\"25\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[25, 0, 0, 0, -24, -24]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{0}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {0}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0099","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"079e2d32f4c4780860c0a84dc65bbcb97123e4abc29b722bfaeffa987d0f8e15","family_id":"qf-statistics-maximal-frequency-set","seed":202610067099,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-25\",\"3\"],[\"1\",\"1\"],[\"26\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[26, 26, 1, -25, -25, -25]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{-25}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {-25}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r07-descriptive-statistics-0100","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1649a1b74af0b529bf961ee13bfbfe3111737d14d497079e8dfef44b03b633c4","family_id":"qf-statistics-maximal-frequency-set","seed":202610067100,"semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-26\",\"1\"],[\"-1\",\"2\"],[\"27\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"},"fields":{"title":"Set of All Maximum-Frequency Observed Values","stem":"The nonempty observation list is D=[27, 27, 27, -1, -1, -26]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.","answer":{"kind":"expression","value":"{27}","explanation":"Count frequencies with all input repetitions retained, then list each maximizing value once. The result is {27}; ties are not broken by choosing just one value, and this stated convention is distinct from textbooks calling an all-distinct list no mode."},"skills":["Set of All Maximum-Frequency Observed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}