統計學 - 十分位數統計

將給定資料或值序列的隨機分佈劃分為十個頻率相似的組的方法稱為十分位數。

公式

${D_i = l + \frac{h}{f}(\frac{iN}{10} - c); i = 1,2,3...,9}$

其中：

問題陳述

根據下表計算分佈的十分位數

解答

$ {\frac{65 \times 1}{10} = 6.5 \\[7pt] \, D_1= 50 + \frac{6.5 - 0}{8} \times 10 , \\[7pt] \, = 58.12}$

$ {\frac{65 \times 2}{10} = 13 \\[7pt] \, D_2= 60 + \frac{13 - 8}{10} \times 10 , \\[7pt] \, = 65}$

$ {\frac{65 \times 3}{10} = 19.5 \\[7pt] \, D_3= 70 + \frac{19.5 - 18}{16} \times 10 , \\[7pt] \, = 70.94}$

$ {\frac{65 \times 4}{10} = 26 \\[7pt] \, D_4= 70 + \frac{26 - 18}{16} \times 10 , \\[7pt] \, = 75}$

$ {\frac{65 \times 5}{10} = 32.5 \\[7pt] \, D_5= 70 + \frac{32.5 - 18}{16} \times 10 , \\[7pt] \, = 79.06}$

$ {\frac{65 \times 6}{10} = 39 \\[7pt] \, D_6= 70 + \frac{39 - 34}{14} \times 10 , \\[7pt] \, = 83.57}$

$ {\frac{65 \times 7}{10} = 45.5 \\[7pt] \, D_7= 80 + \frac{45.5 - 34}{14} \times 10 , \\[7pt] \, = 88.21}$

$ {\frac{65 \times 8}{10} = 52 \\[7pt] \, D_8= 90 + \frac{52 - 48}{10} \times 10 , \\[7pt] \, = 94}$

$ {\frac{65 \times 9}{10} = 58.5 \\[7pt] \, D_9= 100 + \frac{58.5 - 58}{5} \times 10 , \\[7pt] \, = 101}$

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