{"schema_version":"ocme-site-results-v1","locale":"en","page_type":"derivations","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{"q":"mko-descriptive-statistics"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-descriptive-statistics-01","title":{"zh-Hant":"描述統計：保留重數計算平均數、中位數、全距與眾數集合","en":"Descriptive statistics: mean, median, range and mode set with repetitions kept"},"summary":{"zh-Hant":"對觀測列 D=(4,10,1,3,8,1,6,3)，保留重複值，求觀測數 n、算術平均、中位數、全距與本輪約定的眾數集合；證明一般性質「最小值 ≤ 平均 ≤ 最大值」並用它核對；最後說明若先去重會得到不同（錯誤）的平均與中位數。","en":"For the observation list D=(4,10,1,3,8,1,6,3), keeping repeated values, find the number of observations n, the arithmetic mean, the median, the range and the mode set under this entry's convention; prove the general fact 'minimum ≤ mean ≤ maximum' and use it as a check; finally show that deduplicating first would give a different (wrong) mean and median."},"mko_ids":["mko-descriptive-statistics"]}],"title":"Concept derivation guides"}