Finding the median
The median is the middle value in a set of numbers, and it’s a great way to understand typical values without being thrown off by extreme outliers. Whether you're analyzing test scores, the heights of your classmates, or even house prices, finding the median helps you see the "middle ground" in the data. Jump to the questions
Practise now
Calculate the median for each data set below.
Topic guide
What this worksheet practises
This worksheet provides practice on finding the median of a set of data. The median is a type of average that finds the exact physical middle value. It is particularly useful for finding an average of data that contains extreme outliers (like house prices), because the outliers don't skew the result.
Key method
The median is the middle number, but it only works if the data is organised.
- First, write out all the numbers in order from smallest to largest. You cannot skip this step.
- Cross off one number from the left end, and one number from the right end.
- Repeat this process, moving inwards towards the middle.
- If you are left with exactly one number in the middle, that is your median.
- If you are left with exactly two numbers in the middle, the median is the halfway point between them. (Add them together and divide by 2).
Worked example
Find the median of the following set of data: 12, 5, 8, 20, 15, 3.
Step 1: Put the numbers in order from smallest to largest.
3, 5, 8, 12, 15, 20.
Step 2: Cross off the outer pairs.
Cross off 3 and 20. (Leaving 5, 8, 12, 15).
Cross off 5 and 15. (Leaving 8, 12).
Step 3: We have two numbers left in the middle (8 and 12). We must find the number exactly halfway between them.
8 + 12 = 20.
20 ÷ 2 = 10.
The median is 10.
Common mistakes to avoid
The most common and devastating mistake is simply picking the middle number from the list before putting them in size order. In the example above, picking 8 or 20 from the original list is completely incorrect. The data must be ordered first.
Things to remember
A quick formula to find the position of the median in an ordered list is (n + 1) ÷ 2, where 'n' is the total number of items. If you have 9 items, the median is at the (9 + 1) ÷ 2 = 5th position. You still have to put them in order to find what number is actually sitting in that 5th spot.