统计学 - 十分位数统计

将给定数据或值序列的随机分布划分为十个频率相似的组的方法称为十分位数。

公式

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

其中：

问题陈述

根据下表计算分布的十分位数

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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