Median

Median of a group of observation is the value which lies in the middle of the data (when arranged in an ascending or descending order) with half of the observations above it and the other half below it.

When the number of observations (n) is odd.

Then, median is (n + 1)/2 th observation.

When the number of observations (n) is even.

Then median is the mean of (n/2)th and (n + 1/2)th observation.

i.e., Median =
Median

Let us observe the following solved problems using step-by-step explanation.


Worked-out examples on median:

1. Find the median of the data 25, 37, 47, 18, 19, 26, 36.

Solution:

Arranging the data in ascending order, we get 18, 19, 25, 26, 36, 37, 47

Here, the number of observations is odd, i.e., 7.

Therefore, median = (n + 1/2)th observation.

                         = (7 + 1/2)th observation.

                         = (8/2)th observation

                         = 4th observation.

4th observation is 26.

Therefore, median of the data is 26.


2. Find the median of the data 24, 33, 30, 22, 21, 25, 34, 27.

Solution:

Here, the number of observations is even, i.e., 8.

Arranging the data in ascending order, we get 21, 22, 24, 25, 27, 30, 33, 34

Therefore, median = {(n/2)th observation + (n + 1/2)th observation}/2

                         = (8/2)th observation + (8/2 + 1)th observation

                         = 4th observation + (4 + 1)th observation

                         = {25 + 27}/2

                         = 52/2

                         = 26

Therefore, the median of the given data is 26.

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