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 −

  1. ${L}$ = Lower limit of median class, median class is that class where $\frac{n}{2}^{th}$ item is lying.

  2. ${c.f.}$ = Cumulative frequency of the class preceding the median class.

  3. ${f}$ = Frequency of median class.

  4. ${i}$ = 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.

  1. 06 men get less than Rs. 500

  2. 13 men get less than Rs. 1000

  3. 22 men get less than Rs. 1500

  4. 30 men get less than Rs. 2000

  5. 34 men get less than Rs. 2500

  6. 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 −

  1. ${L}$ = 1000

  2. $\frac{n}{2}$ = 20

  3. ${c.f.}$ = 13

  4. ${f}$ = 9

  5. ${i}$ = 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.

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