{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0001","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[0]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"0/1","explanation_zh":"均值=0/1。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067001,"parameters":{"values":[0],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"0\",\"1\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0002","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[-3, -3, -3]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-3/1","explanation_zh":"均值=-3/1。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067002,"parameters":{"values":[-3,-3,-3],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-3\",\"1\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0003","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[-4, 1, 8]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"5/3","explanation_zh":"均值=5/3。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067003,"parameters":{"values":[-4,1,8],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-4\",\"1\"],[\"1\",\"1\"],[\"8\",\"1\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0004","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[-2, -2, 5, 5]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"3/2","explanation_zh":"均值=3/2。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067004,"parameters":{"values":[-2,-2,5,5],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-2\",\"1\"],[\"5\",\"1\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0005","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[-7, -7, 2, 8, 8]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"4/5","explanation_zh":"均值=4/5。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067005,"parameters":{"values":[-7,-7,2,8,8],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-7\",\"2\"],[\"2\",\"1\"],[\"8\",\"2\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0006","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[8, 8, 1, -7, -7, -7]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-2/3","explanation_zh":"均值=-2/3。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067006,"parameters":{"values":[8,8,1,-7,-7,-7],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-7\",\"3\"],[\"1\",\"1\"],[\"8\",\"2\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0007","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[9, 9, 9, -1, -1, -8]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"17/6","explanation_zh":"均值=17/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067007,"parameters":{"values":[9,9,9,-1,-1,-8],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-8\",\"1\"],[\"-1\",\"2\"],[\"9\",\"3\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0008","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[10, 0, 0, 0, -9, -9]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-4/3","explanation_zh":"均值=-4/3。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067008,"parameters":{"values":[10,0,0,0,-9,-9],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-9\",\"2\"],[\"0\",\"3\"],[\"10\",\"1\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0009","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[11, 11, 1, -10, -10, -10]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-7/6","explanation_zh":"均值=-7/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067009,"parameters":{"values":[11,11,1,-10,-10,-10],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-10\",\"3\"],[\"1\",\"1\"],[\"11\",\"2\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0010","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[12, 12, 12, -1, -1, -11]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"23/6","explanation_zh":"均值=23/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067010,"parameters":{"values":[12,12,12,-1,-1,-11],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-11\",\"1\"],[\"-1\",\"2\"],[\"12\",\"3\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0011","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[13, 0, 0, 0, -12, -12]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-11/6","explanation_zh":"均值=-11/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067011,"parameters":{"values":[13,0,0,0,-12,-12],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-12\",\"2\"],[\"0\",\"3\"],[\"13\",\"1\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0012","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[14, 14, 1, -13, -13, -13]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-5/3","explanation_zh":"均值=-5/3。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067012,"parameters":{"values":[14,14,1,-13,-13,-13],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-13\",\"3\"],[\"1\",\"1\"],[\"14\",\"2\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0013","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[15, 15, 15, -1, -1, -14]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"29/6","explanation_zh":"均值=29/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067013,"parameters":{"values":[15,15,15,-1,-1,-14],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-14\",\"1\"],[\"-1\",\"2\"],[\"15\",\"3\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0014","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[16, 0, 0, 0, -15, -15]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-7/3","explanation_zh":"均值=-7/3。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067014,"parameters":{"values":[16,0,0,0,-15,-15],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-15\",\"2\"],[\"0\",\"3\"],[\"16\",\"1\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0015","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[17, 17, 1, -16, -16, -16]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-13/6","explanation_zh":"均值=-13/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067015,"parameters":{"values":[17,17,1,-16,-16,-16],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-16\",\"3\"],[\"1\",\"1\"],[\"17\",\"2\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0016","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[18, 18, 18, -1, -1, -17]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"35/6","explanation_zh":"均值=35/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067016,"parameters":{"values":[18,18,18,-1,-1,-17],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-17\",\"1\"],[\"-1\",\"2\"],[\"18\",\"3\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0017","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[19, 0, 0, 0, -18, -18]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-17/6","explanation_zh":"均值=-17/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067017,"parameters":{"values":[19,0,0,0,-18,-18],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-18\",\"2\"],[\"0\",\"3\"],[\"19\",\"1\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0018","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[20, 20, 1, -19, -19, -19]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-8/3","explanation_zh":"均值=-8/3。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067018,"parameters":{"values":[20,20,1,-19,-19,-19],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-19\",\"3\"],[\"1\",\"1\"],[\"20\",\"2\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0019","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[21, 21, 21, -1, -1, -20]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"41/6","explanation_zh":"均值=41/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067019,"parameters":{"values":[21,21,21,-1,-1,-20],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-20\",\"1\"],[\"-1\",\"2\"],[\"21\",\"3\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0020","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[22, 0, 0, 0, -21, -21]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-10/3","explanation_zh":"均值=-10/3。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067020,"parameters":{"values":[22,0,0,0,-21,-21],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-21\",\"2\"],[\"0\",\"3\"],[\"22\",\"1\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0021","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[23, 23, 1, -22, -22, -22]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-19/6","explanation_zh":"均值=-19/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067021,"parameters":{"values":[23,23,1,-22,-22,-22],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-22\",\"3\"],[\"1\",\"1\"],[\"23\",\"2\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0022","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[24, 24, 24, -1, -1, -23]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"47/6","explanation_zh":"均值=47/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067022,"parameters":{"values":[24,24,24,-1,-1,-23],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-23\",\"1\"],[\"-1\",\"2\"],[\"24\",\"3\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0023","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[25, 0, 0, 0, -24, -24]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-23/6","explanation_zh":"均值=-23/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067023,"parameters":{"values":[25,0,0,0,-24,-24],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-24\",\"2\"],[\"0\",\"3\"],[\"25\",\"1\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0024","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[26, 26, 1, -25, -25, -25]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"-11/3","explanation_zh":"均值=-11/3。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067024,"parameters":{"values":[26,26,1,-25,-25,-25],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-25\",\"3\"],[\"1\",\"1\"],[\"26\",\"2\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0025","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"保留重數的算術平均","stem_zh":"明示非空觀測列 D=[27, 27, 27, -1, -1, -26]，保留重數，所有值為原創合成整數資料。求算術平均，答案為最簡正分母 p/q，整數亦保留 /1。","answer":{"kind":"expression","value":"53/6","explanation_zh":"均值=53/6。每筆觀測都參與總和，再除以觀測筆數；先去重會改變資料，不把摘要當成機率律或母體推論。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["保留重數的算術平均"]},"variant":{"family_id":"qf-statistics-observation-mean","seed":202610067025,"parameters":{"values":[27,27,27,-1,-1,-26],"operation":"observation_mean","semantic_template":"qf-statistics-observation-mean/{\"inputs\":[[\"-26\",\"1\"],[\"-1\",\"2\"],[\"27\",\"3\"]],\"operation\":\"observation_mean\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0026","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[0]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"0/1","explanation_zh":"中位數=0/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067026,"parameters":{"values":[0],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"0\",\"1\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0027","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[-3, -3, -3]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"-3/1","explanation_zh":"中位數=-3/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067027,"parameters":{"values":[-3,-3,-3],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-3\",\"1\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0028","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[-4, 1, 8]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"1/1","explanation_zh":"中位數=1/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067028,"parameters":{"values":[-4,1,8],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-4\",\"1\"],[\"1\",\"1\"],[\"8\",\"1\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0029","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[-2, -2, 5, 5]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"3/2","explanation_zh":"中位數=3/2。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067029,"parameters":{"values":[-2,-2,5,5],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-2\",\"1\"],[\"5\",\"1\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0030","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[-7, -7, 2, 8, 8]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"2/1","explanation_zh":"中位數=2/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067030,"parameters":{"values":[-7,-7,2,8,8],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-7\",\"2\"],[\"2\",\"1\"],[\"8\",\"2\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0031","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[8, 8, 1, -7, -7, -7]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"-3/1","explanation_zh":"中位數=-3/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067031,"parameters":{"values":[8,8,1,-7,-7,-7],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-7\",\"3\"],[\"1\",\"1\"],[\"8\",\"2\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0032","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[9, 9, 9, -1, -1, -8]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"4/1","explanation_zh":"中位數=4/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067032,"parameters":{"values":[9,9,9,-1,-1,-8],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-8\",\"1\"],[\"-1\",\"2\"],[\"9\",\"3\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0033","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[10, 0, 0, 0, -9, -9]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"0/1","explanation_zh":"中位數=0/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067033,"parameters":{"values":[10,0,0,0,-9,-9],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-9\",\"2\"],[\"0\",\"3\"],[\"10\",\"1\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0034","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[11, 11, 1, -10, -10, -10]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"-9/2","explanation_zh":"中位數=-9/2。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067034,"parameters":{"values":[11,11,1,-10,-10,-10],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-10\",\"3\"],[\"1\",\"1\"],[\"11\",\"2\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0035","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[12, 12, 12, -1, -1, -11]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"11/2","explanation_zh":"中位數=11/2。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067035,"parameters":{"values":[12,12,12,-1,-1,-11],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-11\",\"1\"],[\"-1\",\"2\"],[\"12\",\"3\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0036","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[13, 0, 0, 0, -12, -12]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"0/1","explanation_zh":"中位數=0/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067036,"parameters":{"values":[13,0,0,0,-12,-12],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-12\",\"2\"],[\"0\",\"3\"],[\"13\",\"1\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0037","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[14, 14, 1, -13, -13, -13]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"-6/1","explanation_zh":"中位數=-6/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067037,"parameters":{"values":[14,14,1,-13,-13,-13],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-13\",\"3\"],[\"1\",\"1\"],[\"14\",\"2\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0038","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[15, 15, 15, -1, -1, -14]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"7/1","explanation_zh":"中位數=7/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067038,"parameters":{"values":[15,15,15,-1,-1,-14],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-14\",\"1\"],[\"-1\",\"2\"],[\"15\",\"3\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0039","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[16, 0, 0, 0, -15, -15]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"0/1","explanation_zh":"中位數=0/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067039,"parameters":{"values":[16,0,0,0,-15,-15],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-15\",\"2\"],[\"0\",\"3\"],[\"16\",\"1\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0040","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[17, 17, 1, -16, -16, -16]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"-15/2","explanation_zh":"中位數=-15/2。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067040,"parameters":{"values":[17,17,1,-16,-16,-16],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-16\",\"3\"],[\"1\",\"1\"],[\"17\",\"2\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0041","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[18, 18, 18, -1, -1, -17]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"17/2","explanation_zh":"中位數=17/2。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067041,"parameters":{"values":[18,18,18,-1,-1,-17],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-17\",\"1\"],[\"-1\",\"2\"],[\"18\",\"3\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0042","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[19, 0, 0, 0, -18, -18]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"0/1","explanation_zh":"中位數=0/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067042,"parameters":{"values":[19,0,0,0,-18,-18],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-18\",\"2\"],[\"0\",\"3\"],[\"19\",\"1\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0043","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[20, 20, 1, -19, -19, -19]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"-9/1","explanation_zh":"中位數=-9/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067043,"parameters":{"values":[20,20,1,-19,-19,-19],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-19\",\"3\"],[\"1\",\"1\"],[\"20\",\"2\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0044","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[21, 21, 21, -1, -1, -20]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"10/1","explanation_zh":"中位數=10/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067044,"parameters":{"values":[21,21,21,-1,-1,-20],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-20\",\"1\"],[\"-1\",\"2\"],[\"21\",\"3\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0045","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[22, 0, 0, 0, -21, -21]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"0/1","explanation_zh":"中位數=0/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067045,"parameters":{"values":[22,0,0,0,-21,-21],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-21\",\"2\"],[\"0\",\"3\"],[\"22\",\"1\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0046","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[23, 23, 1, -22, -22, -22]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"-21/2","explanation_zh":"中位數=-21/2。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067046,"parameters":{"values":[23,23,1,-22,-22,-22],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-22\",\"3\"],[\"1\",\"1\"],[\"23\",\"2\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0047","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[24, 24, 24, -1, -1, -23]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"23/2","explanation_zh":"中位數=23/2。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067047,"parameters":{"values":[24,24,24,-1,-1,-23],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-23\",\"1\"],[\"-1\",\"2\"],[\"24\",\"3\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0048","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[25, 0, 0, 0, -24, -24]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"0/1","explanation_zh":"中位數=0/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067048,"parameters":{"values":[25,0,0,0,-24,-24],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-24\",\"2\"],[\"0\",\"3\"],[\"25\",\"1\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0049","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[26, 26, 1, -25, -25, -25]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"-12/1","explanation_zh":"中位數=-12/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067049,"parameters":{"values":[26,26,1,-25,-25,-25],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-25\",\"3\"],[\"1\",\"1\"],[\"26\",\"2\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0050","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"奇偶觀測列的精確中位數","stem_zh":"明示非空觀測列 D=[27, 27, 27, -1, -1, -26]，保留重數，所有值為原創合成整數資料。排序後求中位數；偶數筆取中間兩值的平均，答案採最簡正分母 p/q。","answer":{"kind":"expression","value":"13/1","explanation_zh":"中位數=13/1。排序不刪重複觀測；奇數筆取中央值，偶數筆取中央兩值的精確平均，不推論抽樣獨立性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["奇偶觀測列的精確中位數"]},"variant":{"family_id":"qf-statistics-observation-median","seed":202610067050,"parameters":{"values":[27,27,27,-1,-1,-26],"operation":"observation_median","semantic_template":"qf-statistics-observation-median/{\"inputs\":[[\"-26\",\"1\"],[\"-1\",\"2\"],[\"27\",\"3\"]],\"operation\":\"observation_median\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0051","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[0]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"0","explanation_zh":"全距=0。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067051,"parameters":{"values":[0],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"0\",\"0\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0052","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[-3, -3, -3]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"0","explanation_zh":"全距=0。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067052,"parameters":{"values":[-3,-3,-3],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-3\",\"-3\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0053","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[-4, 1, 8]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"12","explanation_zh":"全距=12。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067053,"parameters":{"values":[-4,1,8],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-4\",\"8\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0054","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[-2, -2, 5, 5]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"7","explanation_zh":"全距=7。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067054,"parameters":{"values":[-2,-2,5,5],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-2\",\"5\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0055","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[-7, -7, 2, 8, 8]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"15","explanation_zh":"全距=15。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067055,"parameters":{"values":[-7,-7,2,8,8],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-7\",\"8\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0056","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[9, 9, 9, -1, -1, -8]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"17","explanation_zh":"全距=17。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067056,"parameters":{"values":[9,9,9,-1,-1,-8],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-8\",\"9\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0057","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[10, 0, 0, 0, -9, -9]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"19","explanation_zh":"全距=19。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067057,"parameters":{"values":[10,0,0,0,-9,-9],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-9\",\"10\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0058","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[11, 11, 1, -10, -10, -10]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"21","explanation_zh":"全距=21。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067058,"parameters":{"values":[11,11,1,-10,-10,-10],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-10\",\"11\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0059","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[12, 12, 12, -1, -1, -11]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"23","explanation_zh":"全距=23。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067059,"parameters":{"values":[12,12,12,-1,-1,-11],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-11\",\"12\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0060","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[13, 0, 0, 0, -12, -12]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"25","explanation_zh":"全距=25。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067060,"parameters":{"values":[13,0,0,0,-12,-12],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-12\",\"13\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0061","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[14, 14, 1, -13, -13, -13]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"27","explanation_zh":"全距=27。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067061,"parameters":{"values":[14,14,1,-13,-13,-13],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-13\",\"14\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0062","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[15, 15, 15, -1, -1, -14]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"29","explanation_zh":"全距=29。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067062,"parameters":{"values":[15,15,15,-1,-1,-14],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-14\",\"15\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0063","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[16, 0, 0, 0, -15, -15]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"31","explanation_zh":"全距=31。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067063,"parameters":{"values":[16,0,0,0,-15,-15],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-15\",\"16\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0064","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[17, 17, 1, -16, -16, -16]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"33","explanation_zh":"全距=33。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067064,"parameters":{"values":[17,17,1,-16,-16,-16],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-16\",\"17\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0065","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[18, 18, 18, -1, -1, -17]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"35","explanation_zh":"全距=35。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067065,"parameters":{"values":[18,18,18,-1,-1,-17],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-17\",\"18\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0066","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[19, 0, 0, 0, -18, -18]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"37","explanation_zh":"全距=37。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067066,"parameters":{"values":[19,0,0,0,-18,-18],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-18\",\"19\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0067","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[20, 20, 1, -19, -19, -19]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"39","explanation_zh":"全距=39。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067067,"parameters":{"values":[20,20,1,-19,-19,-19],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-19\",\"20\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0068","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[21, 21, 21, -1, -1, -20]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"41","explanation_zh":"全距=41。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067068,"parameters":{"values":[21,21,21,-1,-1,-20],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-20\",\"21\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0069","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[22, 0, 0, 0, -21, -21]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"43","explanation_zh":"全距=43。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067069,"parameters":{"values":[22,0,0,0,-21,-21],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-21\",\"22\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0070","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[23, 23, 1, -22, -22, -22]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"45","explanation_zh":"全距=45。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067070,"parameters":{"values":[23,23,1,-22,-22,-22],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-22\",\"23\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0071","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[24, 24, 24, -1, -1, -23]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"47","explanation_zh":"全距=47。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067071,"parameters":{"values":[24,24,24,-1,-1,-23],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-23\",\"24\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0072","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[25, 0, 0, 0, -24, -24]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"49","explanation_zh":"全距=49。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067072,"parameters":{"values":[25,0,0,0,-24,-24],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-24\",\"25\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0073","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[26, 26, 1, -25, -25, -25]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"51","explanation_zh":"全距=51。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067073,"parameters":{"values":[26,26,1,-25,-25,-25],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-25\",\"26\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0074","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[27, 27, 27, -1, -1, -26]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"53","explanation_zh":"全距=53。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067074,"parameters":{"values":[27,27,27,-1,-1,-26],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-26\",\"27\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0075","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"觀測列的全距","stem_zh":"明示非空觀測列 D=[28, 0, 0, 0, -27, -27]，保留重數，所有值為原創合成整數資料。求最大觀測值減最小觀測值的全距。","answer":{"kind":"short_text","value":"55","explanation_zh":"全距=55。全距只摘要此列的兩個極值，單筆或全相同觀測的全距零；它不是機率變異數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["觀測列的全距"]},"variant":{"family_id":"qf-statistics-observation-range","seed":202610067075,"parameters":{"values":[28,0,0,0,-27,-27],"operation":"observation_range","semantic_template":"qf-statistics-observation-range/{\"inputs\":[\"-27\",\"28\"],\"operation\":\"observation_range\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0076","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[0]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{0}","explanation_zh":"所有最大頻率值={0}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067076,"parameters":{"values":[0],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"0\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0077","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[-3, -3, -3]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{-3}","explanation_zh":"所有最大頻率值={-3}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067077,"parameters":{"values":[-3,-3,-3],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-3\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0078","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[-4, 1, 8]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{-4, 1, 8}","explanation_zh":"所有最大頻率值={-4, 1, 8}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067078,"parameters":{"values":[-4,1,8],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-4\",\"1\"],[\"1\",\"1\"],[\"8\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0079","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[-2, -2, 5, 5]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{-2, 5}","explanation_zh":"所有最大頻率值={-2, 5}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067079,"parameters":{"values":[-2,-2,5,5],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-2\",\"1\"],[\"5\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0080","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[-7, -7, 2, 8, 8]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{-7, 8}","explanation_zh":"所有最大頻率值={-7, 8}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067080,"parameters":{"values":[-7,-7,2,8,8],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-7\",\"2\"],[\"2\",\"1\"],[\"8\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0081","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[8, 8, 1, -7, -7, -7]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{-7}","explanation_zh":"所有最大頻率值={-7}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067081,"parameters":{"values":[8,8,1,-7,-7,-7],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-7\",\"3\"],[\"1\",\"1\"],[\"8\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0082","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[9, 9, 9, -1, -1, -8]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{9}","explanation_zh":"所有最大頻率值={9}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067082,"parameters":{"values":[9,9,9,-1,-1,-8],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-8\",\"1\"],[\"-1\",\"2\"],[\"9\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0083","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[10, 0, 0, 0, -9, -9]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{0}","explanation_zh":"所有最大頻率值={0}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067083,"parameters":{"values":[10,0,0,0,-9,-9],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-9\",\"2\"],[\"0\",\"3\"],[\"10\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0084","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[11, 11, 1, -10, -10, -10]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{-10}","explanation_zh":"所有最大頻率值={-10}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067084,"parameters":{"values":[11,11,1,-10,-10,-10],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-10\",\"3\"],[\"1\",\"1\"],[\"11\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0085","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[12, 12, 12, -1, -1, -11]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{12}","explanation_zh":"所有最大頻率值={12}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067085,"parameters":{"values":[12,12,12,-1,-1,-11],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-11\",\"1\"],[\"-1\",\"2\"],[\"12\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0086","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[13, 0, 0, 0, -12, -12]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{0}","explanation_zh":"所有最大頻率值={0}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067086,"parameters":{"values":[13,0,0,0,-12,-12],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-12\",\"2\"],[\"0\",\"3\"],[\"13\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0087","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[14, 14, 1, -13, -13, -13]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{-13}","explanation_zh":"所有最大頻率值={-13}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067087,"parameters":{"values":[14,14,1,-13,-13,-13],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-13\",\"3\"],[\"1\",\"1\"],[\"14\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0088","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[15, 15, 15, -1, -1, -14]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{15}","explanation_zh":"所有最大頻率值={15}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067088,"parameters":{"values":[15,15,15,-1,-1,-14],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-14\",\"1\"],[\"-1\",\"2\"],[\"15\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0089","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[16, 0, 0, 0, -15, -15]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{0}","explanation_zh":"所有最大頻率值={0}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067089,"parameters":{"values":[16,0,0,0,-15,-15],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-15\",\"2\"],[\"0\",\"3\"],[\"16\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0090","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[17, 17, 1, -16, -16, -16]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{-16}","explanation_zh":"所有最大頻率值={-16}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067090,"parameters":{"values":[17,17,1,-16,-16,-16],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-16\",\"3\"],[\"1\",\"1\"],[\"17\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0091","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[18, 18, 18, -1, -1, -17]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{18}","explanation_zh":"所有最大頻率值={18}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067091,"parameters":{"values":[18,18,18,-1,-1,-17],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-17\",\"1\"],[\"-1\",\"2\"],[\"18\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0092","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[19, 0, 0, 0, -18, -18]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{0}","explanation_zh":"所有最大頻率值={0}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067092,"parameters":{"values":[19,0,0,0,-18,-18],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-18\",\"2\"],[\"0\",\"3\"],[\"19\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0093","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[20, 20, 1, -19, -19, -19]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{-19}","explanation_zh":"所有最大頻率值={-19}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067093,"parameters":{"values":[20,20,1,-19,-19,-19],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-19\",\"3\"],[\"1\",\"1\"],[\"20\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0094","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[21, 21, 21, -1, -1, -20]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{21}","explanation_zh":"所有最大頻率值={21}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067094,"parameters":{"values":[21,21,21,-1,-1,-20],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-20\",\"1\"],[\"-1\",\"2\"],[\"21\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0095","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[22, 0, 0, 0, -21, -21]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{0}","explanation_zh":"所有最大頻率值={0}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067095,"parameters":{"values":[22,0,0,0,-21,-21],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-21\",\"2\"],[\"0\",\"3\"],[\"22\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0096","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[23, 23, 1, -22, -22, -22]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{-22}","explanation_zh":"所有最大頻率值={-22}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067096,"parameters":{"values":[23,23,1,-22,-22,-22],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-22\",\"3\"],[\"1\",\"1\"],[\"23\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0097","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[24, 24, 24, -1, -1, -23]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{24}","explanation_zh":"所有最大頻率值={24}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067097,"parameters":{"values":[24,24,24,-1,-1,-23],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-23\",\"1\"],[\"-1\",\"2\"],[\"24\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0098","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[25, 0, 0, 0, -24, -24]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{0}","explanation_zh":"所有最大頻率值={0}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067098,"parameters":{"values":[25,0,0,0,-24,-24],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-24\",\"2\"],[\"0\",\"3\"],[\"25\",\"1\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0099","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[26, 26, 1, -25, -25, -25]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{-25}","explanation_zh":"所有最大頻率值={-25}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067099,"parameters":{"values":[26,26,1,-25,-25,-25],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-25\",\"3\"],[\"1\",\"1\"],[\"26\",\"2\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r07-descriptive-statistics-0100","batch_id":"batch-20261005-advance-20261006-r07-descriptive-statistics-foundations","language":"zh-Hant","source_mko_ids":["mko-descriptive-statistics"],"title_zh":"全部最大頻率觀測值的集合","stem_zh":"明示非空觀測列 D=[27, 27, 27, -1, -1, -26]，保留重數，所有值為原創合成整數資料。本題明示眾數集合慣例為所有達最大出現頻率的值；即使各值只出現一次也全部列出。求集合，按值遞增且每值只列一次。","answer":{"kind":"expression","value":"{27}","explanation_zh":"所有最大頻率值={27}。先保留重數計各值頻率，再同時列出所有並列最大者；本慣例不要求唯一眾數，也不否定其他教材的無眾數用語。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全部最大頻率觀測值的集合"]},"variant":{"family_id":"qf-statistics-maximal-frequency-set","seed":202610067100,"parameters":{"values":[27,27,27,-1,-1,-26],"mode_convention":"all_frequency_maximizers","operation":"maximal_frequency_set","semantic_template":"qf-statistics-maximal-frequency-set/{\"inputs\":[[\"-26\",\"1\"],[\"-1\",\"2\"],[\"27\",\"3\"]],\"operation\":\"maximal_frequency_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}