# Median Math

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Definition: - Median is the central value of the arranged data either in ascending or descending order.

Hence median is the 50th percentile of a data which divides the whole data in two equal portions.

Example: - The following data give the weight (in pounds) lost by 15 new members of a health club at the end of their first two months of membership.

5          10        8          7          25        12        5          14
11        10        21        9          8          11        18

Find the median.

Solution: -

Step 1:- Arrange the data.
5          5          7          8          8          9          10        10
11        11        12        14        18        21        25

Step 2:- Find (n+1)/2                          Where n= number of values in a data
(n+1) / 2 = (15+1)/ 2
= 16 / 2
= 8

This shows that 8th position is the median value.

Step 3:- Value at the 8th position = 10
5          5          7          8          8          9          10        10
11        11        12        14        18        21        25

Median = 10

Example 2:- The following data give the numbers of cars theft that occurred in a city in the past 12 days.

6          3          7          11        4          3          8          7          2          6          9          15

Solution: - Arrange data is
2          3          3          4          6          6          7          7          8          9          11        15

It is an even data: n= 12 so the median will be the average of two central values.
(n+1) /2 =(12+1)/2 = 6.5

6th and 7th positions are the median value.

Median= (6+7)/2= 6.5