{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261005-advance-20261006-r07-descriptive-statistics-0030", "pilot_number": "R0056-28955", "number": 28955, "family_id": "qf-statistics-observation-median", "title": { "zh-Hant": "第 28955 題：奇偶觀測列的精確中位數", "en": "Question 28955: Exact Median of an Odd or Even Observation List" }, "original_question": { "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" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261005-advance-20261006-r07-descriptive-statistics-0030", "batch_id": "batch-20261005-advance-20261006-r07-descriptive-statistics-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "5e3d4de7bb55591e717fc7f7e60b64c24b201bb5fae8f3f622d0605e59cccffa", "family_id": "qf-statistics-observation-median", "seed": 202610067030, "semantic_template": "qf-statistics-observation-median/{\"inputs\":[[\"-7\",\"2\"],[\"2\",\"1\"],[\"8\",\"2\"]],\"operation\":\"observation_median\"}" }, "fields": { "title": "Exact Median of an Odd or Even Observation List", "stem": "The nonempty observation list is D=[-7, -7, 2, 8, 8]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers.", "answer": { "kind": "expression", "value": "2/1", "explanation": "The sorted list retaining repetitions is [-7, -7, 2, 8, 8]. Apply the stated odd/even convention to obtain 2/1; the even-length median need not be an observed value." }, "skills": [ "Exact Median of an Odd or Even Observation List" ], "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review." } }, "givens": [ { "id": "G001", "text": { "zh-Hant": "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。", "en": "The nonempty observation list is D=[-7, -7, 2, 8, 8]. Retain every repetition. Find the median after sorting: one middle value for odd length, or the average of the two middle values for even length. Give a reduced fraction with positive denominator, retaining /1 for integers." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-statistics-observation-median, observation_median]", "after": "derived = [odd_middle_or_even_two_middle_mean]", "relation": "implies", "rule_id": "R56_source_answer_role_and_EXACT_family_interface", "conditions": [], "explanation": { "zh-Hant": "本題輸出依原scalar／set／是非／fraction角色；有理數整數保留/1。不加未宣告domain，不改中英來源、公式或題目。", "en": "Use the declared scalar/set/Yes-No/fraction answer role;integer fractions retain/1.Do not add an undeclared domain or change original bilingual data,formulas or questions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向逐項代回原始資料與本步條件；保持索引、符號、嚴格／非嚴格邊界，不能用正確答案代替推導責任。這是候選教學與精確核對，非形式證明或發布資格。", "en": "Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [[-7, -7, 2, 8, 8]]", "after": "derived = [[-7, -7, 2, 8, 8], 5]", "relation": "implies", "rule_id": "Statistics_FULL_observations_MULTIPLICITY_and_numeric_order", "conditions": [], "explanation": { "zh-Hant": "每次觀測都保留，包括相同數值的重複。numeric排序只改順序，不變n或總和；不能用set先去重，也不能lexical排序。只陳述本樣本，不推母體規律。", "en": "Retain EVERY observation,including repeated values.Numeric sorting changes order only,not n or the sum;do not deduplicate as a set or sort lexically.These are sample summaries,not inferred population laws." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向逐項代回原始資料與本步條件；保持索引、符號、嚴格／非嚴格邊界，不能用正確答案代替推導責任。這是候選教學與精確核對，非形式證明或發布資格。", "en": "Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [[-7, -7, 2, 8, 8], 5]", "after": "derived = [2, 2]", "relation": "implies", "rule_id": "Statistics_ODD_median_actual_middle_order_statistic", "conditions": [], "explanation": { "zh-Hant": "奇數n取從0編號n//2的中間order statistic，兩側各(n-1)/2個；不可誤用原未排序index。", "en": "For odd n use sorted zero-based index n//2,with(n-1)/2 entries on each side,not the original unsorted index." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向逐項代回原始資料與本步條件；保持索引、符號、嚴格／非嚴格邊界，不能用正確答案代替推導責任。這是候選教學與精確核對，非形式證明或發布資格。", "en": "Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance." } }, "arithmetic": null } ], "math_model": { "result": "2/1" }, "conclusion": { "canonical_value": "2/1", "explanation": { "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。", "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged." } }, "definition_note": { "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。", "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate." }, "source": { "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db", "question_binding": { "batch_id": "batch-20261005-advance-20261006-r07-descriptive-statistics-foundations", "batch_path": "public/data/questions/batches/batch-20261005-advance-20261006-r07-descriptive-statistics-foundations/questions.jsonl", "batch_sha256": "747ab8e474f0b3e38444e9bf7afff58120ac1b324b06ceb99e7b56747bcb3a70", "original_line": 30, "original_line_sha256": "bde773f8c86b93f929651317dce1b1129524ef8e7516d53578bfd2effb1615a7", "question_compact_sha256": "5e3d4de7bb55591e717fc7f7e60b64c24b201bb5fae8f3f622d0605e59cccffa", "english_row_compact_sha256": "68cf44d726e31cb16f1ce673ab1dd6711461b7bb289a57483529994606c65909", "english_manifest_path": "public/data/i18n/editions/batch-20261005-advance-20261006-r07-descriptive-statistics-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261005-advance-20261006-r07-descriptive-statistics-foundations.en.jsonl" }, "mko_bindings": { "mko-descriptive-statistics": { "sha256": "bb188b4a4f67bc4e07da170bd9ea1b92aa0a51719cac24e1570cb156d8f76204", "english_sha256": "54dad0cd96ba57e6ace6bc691c6895d71b99feca5b90a348806c619d275baffe", "original_path": "public/data/mko/descriptive-statistics.json", "english_path": "public/data/i18n/editions/mko-descriptive-statistics.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "e340023047850507ee3fe2ae1466d606cfcbd26849aa3bb168d53248f38097e5", "original_candidate_sha256": "12a37e752653cd7014e21798a76bdf623a59d4696e0b79118790080096131ef6", "original_candidate_line_sha256": "12a37e752653cd7014e21798a76bdf623a59d4696e0b79118790080096131ef6" }, "historical_source_state": { "review_state": { "derivation": "candidate_authored_and_locally_checked", "source_question_state": "candidate", "independent_AI_or_human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN" }, "scope_note": { "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。", "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged." }, "label": "Frozen producer metadata; current per-question review is separate below." }, "revision": { "id": "review-20261026-010-p57", "review_date": "2026-10-26", "owner_authorized_reader_publication": true, "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.", "review_receipts": { "semantic_review_sha256": "8bbda4edbed7078634ae88342998c79bcfb95de96187fac119c3b08e0adb0bc8", "question_first_witness_sha256": "3edafa72d63d16a22414892b55806430e0a25b15b926d04f312550179607759f" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 3, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "90af67d8ab2845d41ffebe85785ef695a810a380933ea7ae2d557c0dfa2bc5db", "arithmetic_steps": 0 }, "uses_answer_as_premise": false, "human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN", "Canonical_truth_promotion": false, "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged." } }