Statistics - Continuous Series Arithmetic Median

When data is given based on ranges along with their frequencies. Following is an example of continous series −

Formula

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.

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 −

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 −

Given are the cumulative frequencies of the workers. Hence we first find the simple frequency and present the data in tabular form.

In order to simplify the calculation, a common factor i = 500 has been taken. Using the following formula for calculating median wage.

Where −

• ${L}$ = 1000

• $\frac{n}{2}$ = 20

• ${c.f.}$ = 13

• ${f}$ = 9

• ${i}$ = 500

Thus

As 1388.9 ≃ 1389.

The median wage is Rs. 1389.

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