1. Calculating the median
The Median is found by listing the data points in numerical order and selecting the middle number.
Example
Find the median for the set of numbers 3, 1, 4, 7, 8, 1, 9
Find the median for the set of numbers 8, 7, 3, 4, 4, 8, 6, 2, 1, 5
Sally’s last 8 maths tests are as listed below. Find her median score

2. In general to find the median we could add one to the number of data points and divide by two. This value will tell you where the median is found.
e.g. in the first example above there were 7 data points therefore (7+1)/2 = 4 i.e. the median is found at the 4th data point.

3. Example
Michael’s last 10 maths tests are as listed below. Find his median score.
Here the median is found at (10+1)/2 = 5.5th position! This means that the median is found between the 5th and 6th position.

4. Calculating the quartiles
To find the lower quartile we simply divide the data into two halves to find the median and then divide each half into half again to give Q1 (the lower quartile) and Q3 the upper quartile.
Example
Find the quartiles for the set of numbers 3, 1, 4, 7, 8, 1, 9
Find the quartiles for the set of numbers 8, 7, 3, 4, 4, 8, 6, 2, 1, 5
Sally’s last 8 maths tests are as listed below. Find the lower and upper quartile.