Statistics 简明教程
Statistics - Quartile Deviation
它取决于下四分位数 ${Q_1}$ 和上四分位数 ${Q_3}$。差值 ${Q_3 - Q_1}$ 称为四分位距。差值 ${Q_3 - Q_1}$ 除以 2 称为半四分位距或四分位离差。
It depends on the lower quartile ${Q_1}$ and the upper quartile ${Q_3}$. The difference ${Q_3 - Q_1}$ is called the inter quartile range. The difference ${Q_3 - Q_1}$ divided by 2 is called semi-inter quartile range or the quartile deviation.
Coefficient of Quartile Deviation
基于四分位离差的分散度相对测量称为四分位离差系数。其特征如下：
A relative measure of dispersion based on the quartile deviation is known as the coefficient of quartile deviation. It is characterized as
Example
Problem Statement:
Problem Statement:
从下面给出的数据计算四分位离差和四分位离差系数：
Calculate the quartile deviation and coefficient of quartile deviation from the data given below:
Maximum Load (short-tons) |
Number of Cables |
9.3-9.7 |
22 |
9.8-10.2 |
55 |
10.3-10.7 |
12 |
10.8-11.2 |
17 |
11.3-11.7 |
14 |
11.8-12.2 |
66 |
12.3-12.7 |
33 |
12.8-13.2 |
11 |
Solution:
Solution:
Maximum Load (short-tons) |
Number of Cables (f) |
Class Bounderies |
Cumulative Frequencies |
9.3-9.7 |
2 |
9.25-9.75 |
2 |
9.8-10.2 |
5 |
9.75-10.25 |
2 + 5 = 7 |
10.3-10.7 |
12 |
10.25-10.75 |
7 + 12 = 19 |
10.8-11.2 |
17 |
10.75-11.25 |
19 + 17 = 36 |
11.3-11.7 |
14 |
11.25-11.75 |
36 + 14 = 50 |
11.8-12.2 |
6 |
11.75-12.25 |
50 + 6 = 56 |
12.3-12.7 |
3 |
12.25-12.75 |
56 + 3 = 59 |
12.8-13.2 |
1 |
12.75-13.25 |
59 + 1 = 60 |
${Q_1}$
${\frac{n}{4}^{th}}$ 项的值 = ${\frac{60}{4}^{th}}$ 项的值 = 第 ${15^{th}}$ 项。因此，${Q_1}$ 介于 10.25-10.75 类。
Value of ${\frac{n}{4}^{th}}$ item =Value of ${\frac{60}{4}^{th}}$ thing = ${15^{th}}$ item. Thus ${Q_1}$ lies in class 10.25-10.75.