how do i get the median if the no of observations are even - Maths - Data Handling

Question

how do i get the median if the no of observations are even

Ankush Jain · Accepted Answer

$If n is even, then median = \frac{value of (\frac{n}{2})^{th} observation + value of (\frac{n}{2} + 1)^{th} observation}{2}$

Take an example of following data:

25, 34, 31, 23, 22, 26, 35, 28, 20, 32

we have to find median of given data.

Arrange the data in ascending order, we get 20, 22, 23, 25, 26, 28, 31, 32, 34, 35

Here, the number of observation, n = 10 (even)

$∴ median = \frac{Value of {\frac{n}{2}}^{th} observation + Value of (\frac{n}{2} + 1)^{th} observation}{2} = \frac{value of (\frac{10}{2})^{th} {observation + value of (\frac{10}{2} + 1)}^{th} observation}{2} = \frac{value of 5^{th} {observation + value of 6}^{th} observation}{2} median = \frac{26 + 28}{2} = 27$

Hence, median is 27 of given data.

how do i get the median if the no. of observations are even.