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

Posted by

DrGaurav

On January 31, 2024

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 5.5^th term

To find the median, add the 5^th and 6^th 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 4^th 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 4^th observation

Median = 20

Example 3:

Find the median monthly income of 12 families provided below.

Median in Individual Series

Solution:

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

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

= Size of 6.5^th item

To find the median, add the 6^th and 7^th 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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Calculation of Median in Individual Series | Formula of Median | Statistics