Statistics 简明教程
Statistics - Continuous Series Arithmetic Median
当提供基于范围及其频率性的数据时。下面是连续数列示例 −
When data is given based on ranges along with their frequencies. Following is an example of continous series −
Items |
0-5 |
5-10 |
10-20 |
20-30 |
30-40 |
Frequency |
2 |
5 |
1 |
3 |
12 |
Formula
其中——
Where −
-
${L}$ = Lower limit of median class, median class is that class where $\frac{n}{2}^{th}$ item is lying.
-
${c.f.}$ = Cumulative frequency of the class preceding the median class.
-
${f}$ = Frequency of median class.
-
${i}$ = Class interval of median class.
对于数据类型为标称数据的情况，算术中位数是中心趋势的有用度量。由于它是一个位置平均值，因此不受极端值的影响。
Arithmetic Median is a useful measure of central tendency in case the data type is nominal data. Since it is a positional average, it does not get affected by extreme values.
Example
Problem Statement −
Problem Statement −
在一个组织中进行的一项研究中，观察到工人工资收入的分布情况。找出该组织工人工资的中位数。
In a study conducted in an organization, the distribution of income across the workers is observed. Find the the median wage of the workers of the organization.
-
06 men get less than Rs. 500
-
13 men get less than Rs. 1000
-
22 men get less than Rs. 1500
-
30 men get less than Rs. 2000
-
34 men get less than Rs. 2500
-
40 men get less than Rs. 3000
Solution −
Solution −
提供的是工人的累积频率。因此，我们首先找到简单的频率，并将数据显示在表格中。
Given are the cumulative frequencies of the workers. Hence we first find the simple frequency and present the data in tabular form.
Income (rs.) |
M.P. m |
Frequency f |
(m-1250)/500 d |
fd |
c.f |
0 - 500 |
250 |
6 |
-2 |
-12 |
6 |
500 - 1000 |
750 |
7 |
-1 |
-7 |
13 |
1000 - 1500 |
1250 |
9 |
0 |
0 |
22 |
1500 - 2000 |
1750 |
8 |
1 |
8 |
30 |
2000 - 2500 |
2250 |
4 |
2 |
8 |
34 |
2500 - 3000 |
2750 |
6 |
3 |
18 |
40 |
N = 40 |
∑ fd = 15 |
为了简化计算，采取了公因子 i = 500。使用计算中位数工资的以下公式。
In order to simplify the calculation, a common factor i = 500 has been taken. Using the following formula for calculating median wage.
其中——
Where −
-
${L}$ = 1000
-
$\frac{n}{2}$ = 20
-
${c.f.}$ = 13
-
${f}$ = 9
-
${i}$ = 500
因此
Thus
当 1388.9 ≃ 1389 时。
As 1388.9 ≃ 1389.
中位数工资为 1389 卢比。
The median wage is Rs. 1389.