统计数据 - 统计十分位数
将一系列数据或值的给定随机分布划分为十组相似频率的系统被称为十进制。
式
$ {D_i = l + \\ frac {h} {f}（\\ frac {iN} {10} - c）; i = 1,2,3 ...，9}
其中 -
$ {l} $ =十进制组的下边界。
$ {h} $ =十进制组宽度。
$ {f} $ =十进制组的频率。
$ {N} $ =观察总数。
$ {c} $ =累计频率前十进制组。
例子
问题陈述:
计算下表的分布的十分位数:
| fi | Fi | |
|---|---|---|
| [50-60] | 8 | 8 |
| [60-60] | 10 | 18 |
| [70-60] | 16 | 34 |
| [80-60] | 14 | 48 |
| [90-60] | 10 | 58 |
| [100-60] | 5 | 63 |
| [110-60] | 2 | 65 |
| 65 |
解决方案:
Calculation of First Decile
$ {\frac{65 \times 1}{10} = 6.5 \\[7pt]
\, D_1= 50 + \frac{6.5 - 0}{8} \times 10 , \\[7pt]
\, = 58.12}$
Calculation of Second Decile
$ {\frac{65 \times 2}{10} = 13 \\[7pt]
\, D_2= 60 + \frac{13 - 8}{10} \times 10 , \\[7pt]
\, = 65}$
Calculation of Third Decile
$ {\frac{65 \times 3}{10} = 19.5 \\[7pt]
\, D_3= 70 + \frac{19.5 - 18}{16} \times 10 , \\[7pt]
\, = 70.94}$
Calculation of Fourth Decile
$ {\frac{65 \times 4}{10} = 26 \\[7pt]
\, D_4= 70 + \frac{26 - 18}{16} \times 10 , \\[7pt]
\, = 75}$
Calculation of Fifth Decile
$ {\frac{65 \times 5}{10} = 32.5 \\[7pt]
\, D_5= 70 + \frac{32.5 - 18}{16} \times 10 , \\[7pt]
\, = 79.06}$
Calculation of Sixth Decile
$ {\frac{65 \times 6}{10} = 39 \\[7pt]
\, D_6= 70 + \frac{39 - 34}{14} \times 10 , \\[7pt]
\, = 83.57}$
Calculation of Seventh Decile
$ {\frac{65 \times 7}{10} = 45.5 \\[7pt]
\, D_7= 80 + \frac{45.5 - 34}{14} \times 10 , \\[7pt]
\, = 88.21}$
Calculation of Eighth Decile
$ {\frac{65 \times 8}{10} = 52 \\[7pt]
\, D_8= 90 + \frac{52 - 48}{10} \times 10 , \\[7pt]
\, = 94}$
Calculation of Nineth Decile
$ {\frac{65 \times 9}{10} = 58.5 \\[7pt]
\, D_9= 100 + \frac{58.5 - 58}{5} \times 10 , \\[7pt]
\, = 101}$