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第 21 週 · 離差度量與統計 · 第 6 節（畢業）

抽樣、統計的應用與誤用

整套課程最後一節！前面學的是「怎麼算統計量」，這節學「怎麼<u>正確用</u>統計、怎麼<u>識破</u>統計騙局」—— 學完就畢業。配滿圖例，帶你看穿截斷縱軸、相關≠因果、誇大圖。

▶ 第一關： 總體、樣本與抽樣方法
population (all)sample(a subset)study the sample, infer the whole population
three sampling methods1. simple random2. systematic (every 3rd)3. stratified (by group)group Agroup Bfilled = picked / grey = not picked
▶ 第二關： 問卷信度·效度與抽樣偏差
reliability vs validity (dartboard)high reliab. / low valid.tight but off-targethigh reliab. / high valid.tight AND on-target (best)low reliab. / low valid.scattered and off (worst)low reliab. / high valid.scattered, avg near center
volunteer bias (self-selected sample)the whole populationonly volunteers replyfans & haters answer, ordinary people do not
▶ 第三關： 識破誤導性統計
same data, two y-axes0ABy from 0: tiny gap100ABy from 100: huge gap!
correlation is NOT causationwarmer weather →ice creamdrowningcommon cause = heat
value doubles (1 → 2), but...value = 1area = 1value = 2area = 4 (not 2!)scaling width AND height exaggerates
tiny sample = unreliableasked only 5 people4/5 = 80%? one more vote → 67%too small to represent everyone
⚔ BOSS（畢業終關）： 看穿陷阱 + 全課回顧
your full HKDSE Maths journey— junior foundation (W0-W8) —W0-2 number/algebraW3-4 coord/geometryW5-6 solid/statW7 DSE gapsW8 base fix— senior compulsory (W9-W21) —W9 quad eqnW10 quad fnW11 polynomialW12 simul/varW13 exp/logW14 sequencesW15 inequalW16 circlesW17 coord geoW18 trig (1)W19 trig (2)W20 perm/probW21 dispersion/statGRADUATED!now go practice past paperszero to full compulsory syllabus