Key takeaways
- The median is the middle value after you sort the numbers from smallest to largest.
- Odd count: take the middle number. Even count: average the two middle numbers.
- Always sort first. The middle of an unsorted list is meaningless.
- The median is barely affected by very large or very small values.
In this guide
What is the median?
Imagine five children standing in a line from shortest to tallest. The child in the middle position has the median height. Half the group is shorter and half is taller.
The median is one of three common kinds of average, together with the mean and the mode.
Why does the median matter?
The mean uses every value, so one extreme number can drag it far away from the typical value. The median only cares about the middle, so it stays steady.
In the list 1, 2, 3, 4 and 100, the mean is 22 but the median is 3. Which one better describes the list? The median.
That is why salaries, house prices and waiting times are usually reported as medians.
The formula
| Symbol | What it means | Example |
|---|---|---|
| n | How many numbers are in the list | 6 |
| (n + 1) ÷ 2 | The middle position | 3.5 |
| Median | The middle value | 6 |
If the position is a whole number (odd n), the median is the value in that position. If it ends in .5 (even n), the median is the average of the two values either side of it. Position 3.5 means: average the 3rd and 4th values.
How to find the median step by step
- 1Sort the numbers. Write them from smallest to largest.
- 2Count them. This is n.
- 3Odd count? Pick the number in position
(n + 1) ÷ 2. - 4Even count? Take the two middle numbers, add them and divide by 2.
Type your own numbers into the calculator below, separated by commas, and it will sort them and find the middle for you.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Dropping repeated values. In 2, 2, 3 both 2s count. The median is 2.
- Picking one number for an even count. With an even count you must average the two middle values.
- Giving the position instead of the value. Position 3 is not the median. The number in position 3 is.
Tips and tricks
- Compare mean and median. If the mean is much bigger than the median, a few very large values are pulling it up.
- The median can be a new number. For an even count it may not appear in your list at all.
- Want to see the spread too? The range calculator gives the gap between the smallest and largest value.
Where you'll use it in real life
- Housing: median house prices and rents in a city.
- Jobs: median salary, which is not pulled up by a few very high earners.
- School: a typical test score when a few students scored very high or very low.
- Health: median waiting times at a hospital or clinic.
Quick summary
To find the median, sort your numbers and pick the middle one. With an even count, average the two middle numbers. Use the calculator above to sort your list and find the median with every step shown.
Worked example
You recorded how many minutes you spent on homework over six days: 7, 3, 9, 5, 12 and 4. You want the middle value.
- 01Ordered set: 3, 4, 5, 7, 9, 12
- 02Even number of values: median = average of 5 and 7
- 03Median = 6
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I find the median of an even set of numbers?
Sort the numbers and take the two in the middle. Add them and divide by 2. For 3, 4, 5, 7, 9, 12 the middle pair is 5 and 7, so the median is 6.
What is the difference between median and mean?
The mean adds all values and divides by the count. The median is simply the middle value after sorting. One very large number changes the mean a lot but barely moves the median.
Can the median be a number that is not in the list?
Yes. When the count is even, the median is the average of two values, so it may not appear in the data. The median of 1, 2, 3, 4 is 2.5.
