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第 21 週 · 離差度量與統計 · 第 1 節

離差·分佈域·四分位距

最後一週！光知道「中間在哪」（平均、中位數）不夠，還要知道「數據散得有多開」。這節用分佈域和四分位距把「離差」講透，配滿圖例。

▶ 第一關： 離差與分佈域
A: tightB: spreadsame mean 50, very different spread
min 3max 12range = max − min = 9
2 4 6 8100range = 100 - 2 = 98one outlier inflates the range
▶ 第二關： 四分位數與 IQR
Q₁Q₂Q₃25%25%25%25%three cuts split data into four equal parts
2 4 6 | 8 | 10 12 14Q₁=4Q₂=8Q₃=12IQR = Q₃ − Q₁ = 12 − 4 = 8
1 3 5 7 | 9 11 13 15Q1=(3+5)/2=4Q2=(7+9)/2=8Q3=(11+13)/2=12even count: average the middle two
▶ 第三關： 分佈域 vs 四分位距
outlierrange: huge (pulled by outlier)IQR: still small (ignores the outlier)IQR is robust to extreme values
range = 14 (full spread)IQR = 8 (middle 50%)IQR is at most the range
⚔ BOSS： 四分位距綜合