Math Statistics: Median

Given a set of observations, the median is the middle value among the observations. To find the median, you must first arrange the observations in an ascending (or descending) order.

There are 2 possible cases to consider in finding the median.

Case 1. When the number of observations is odd, the median is the middle value.

Example:

Find the median of the following set of points in a game:

15, 14, 10, 8, 12, 8, 16

Solution:

First arrange the point values in an ascending order.

8, 8, 10, 12, 14, 15, 16

The number of point values is 7, an odd number. Hence the median is the value in the middle position.

Median = 12

Case 2. When the number of observations is even, the median is the average of the two middle values.

Example:

Find the median of the following set of points:

15, 14, 10, 8, 12, 8, 16, 13

Solution:

First arrange the point values in an ascending order.

8, 8, 10, 12, 13, 14, 15, 16

The number of point values is 8, an even number. Hence the median is the average of the 2 middle values.

Sometimes, you may be asked to determine the possible values of the median of a set of numbers.

Example:

x is the median for 4, 3, 8, x and 7. Find the possible values for x.

Solution:

Arrange the numbers in ascending order with x in the middle.

3, 4, x, 7, 8

This tells us that the possible values of x are 4, 5, 6 and 7.

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