Calculation of Median in Individual Series | Formula of Median | Statistics

Calculation of media in individual series - When elements in the data set are organized sequentially odd and even series Median Formula

What is the Median?

Calculation of media in individual series – Formula of Median | When elements in the data set are organized sequentially, that is, in either an ascending or descending order of magnitude, the median can be referred to as the middle value of the data set. Its value is located in a distribution in such a way that 50% of the items are below it and 50% are above it. It focuses on the center or middle of a distribution.

What is an Individual Series?

The series in which the items are listed singly is known as Individual Series. In simple terms, a separate value of the measurement is given to each item. 

Example of Individual Series

If the marks of 5 students of Class XI is given individually as, 70, 82, 65, 95, and 90; then, the resultant series will be an individual series. 

Calculation of Median in Individual Series

The steps required to determine the median of an individual series are as follows:

Step 1: Firstly, arrange the given data in ascending or descending order.

Step 2: Apply the following formula for the Median:

Median(M)=Size~of~[\frac{N+1}{2}]^{th}~item

Where, 

N is the Number of Items

The median in case of Odd and Even Number of Items

In case of odd number of items, the Median is the Middle term of the observation. However, in the case of an even number of items, the Median is the average of two middle terms and is determined by using the following formula:

Median(M)=\frac{Size~of~[\frac{N}{2}]^{th}~item+Size~of~[\frac{N}{2}+1]^{th}~item}{2}

Example 1:

In a football game, 10 players scored the following number of goals: 4, 1, 2, 6, 10, 8, 11, 3, 9, 7.

Find the median of the data.

Solution:

Data provided: 4, 1, 2, 6, 10, 8, 11, 3, 9, 7.

Now sort the information into the following ascending order: 1, 2, 3, 4, 6, 7, 8, 9, 10, 11.

There are 10 observations in this case, which is an even number.

Median(M)=Size~of~[\frac{N+1}{2}]^{th}~item

Median(M)=Size~of~[\frac{10+1}{2}]^{th}~item

Median = Size of 5.5th term

To find the median, add the 5th and 6th items together and then divide the sum by 2.

Median(M)=\frac{Size~of~5^{th}~item+Size~of~6^{th}~item}{2}

=\frac{6+7}{2}=\frac{13}{2}=6.5

Median = 6.5

Example 2:

Calculate the median of 9, 17, 13, 30, 18, 25, and 20. Find the new median if the number 13 is replaced with the number 31.

Solution:

Arrange the given data in ascending order, 9, 13, 17, 18, 20, 25, 30.

There are 7 observations, which is an odd number.

Median(M)=Size~of~[\frac{N+1}{2}]^{th}~item

Median(M)=Size~of~[\frac{7+1}{2}]^{th}~item

Median = Size of 4th observation

Median = 18

When 13 is replaced by 31, the following data is obtained when arranged in ascending order: 9, 17, 18, 20, 25, 30, 31.

Now,

Median = Size of 4th observation

Median = 20

Example 3:

Find the median monthly income of 12 families provided below.

Median in Individual Series

Solution:

Median in Individual Series

Median(M)=Size~of~[\frac{N+1}{2}]^{th}~item

Median(M)=Size~of~[\frac{12+1}{2}]^{th}~item

= Size of 6.5th item

To find the median, add the 6th and 7th items together and then divide the sum by 2.

Median(M)=\frac{Size~of~6^{th}~item+Size~of~7^{th}~item}{2}

=\frac{1,700+2,000}{2}=\frac{3,700}{2}=1,850

Median = 1,850


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Written by 

Dr. Gaurav has a doctorate in management, a NET & JRF in commerce and management, an MBA, and a M.COM. Gaining a satisfaction career of more than 10 years in research and Teaching as an Associate professor. He published more than 20 textbooks and 15 research papers.

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