GCSE Maths Revision: Interquartile Range

4th April 2017

New GCSE Maths Syllabus

Algebra - Interquartile Range - The Key Information!


To help you do the very best in your maths exams, we’ll be going through the main points you should being revising for working out and understanding the interquartile range. As well as this we will go through the lower quartile and upper quartile, both of which are needed to work out the interquartile range.

The interquartile range is the middle 50% of any given data. To find this we have to take away the lower quartile from the upper quartile.

Interquartile range = upper quartile - lower quartile.


An example could be analysing the weights of 5 different cakes:
1.5kg, 0.7kg, 0.4kg, 1.8kg, 2kg, 2.2kg, 2.5kg


Here you need to find the interquartile range of the weights of the cakes.


First we find the median by adding 1 to the total number of pieces of data. In this example there are 7 cakes so we add 1 to this to get 8. We then divide this by 2 to get 4. This means the fourth cake is the median.


The cakes in weight order are 0.4kg, 0.7kg, 1.5kg, 1.8kg, 2kg 2.2kg, 2.5kg meaning 1.8kg is the fourth and consequently the mediant.


We use a similar method to find the lower quartile but instead divide by 4 rather than 2. In our example this would be 8/4 which is 2. The second weight is our lower quartile which is 0.7kg.


To find the upper quartile we times the lower quartile by 3. This is because ¼ x 3 = ¾. This would be 2 x 3 to get 6, meaning the 6th cake is the upper quartile which is 2.2kg.

Finally, to find the interquartile range we have to subtract the lower quartile from the upper quartile. In our example this would be 2.2kg - 0.7kg meaning the interquartile range of the weights of the cakes is 1.5kg!

Everything we’ve gone through in this factsheet can also be found in our interquartile range song which will help you remember all of this information. Be sure to give it a listen!


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