How to Calculate the Average (Mean, Median and Mode)

"Average" usually means the mean, but statistics offers three common ways to find the middle of a list. Each answers a slightly different question.

Worked example

Take these six numbers: 12, 15, 18, 15, 22, 30.

Mean

Add them all up and divide by how many there are.

Mean = sum ÷ count
Sum = 12 + 15 + 18 + 15 + 22 + 30 = 112
Mean = 112 ÷ 6 = 18.67

Median

Sort the numbers, then take the middle one. With an even count, average the two in the middle.

Sorted: 12, 15, 15, 18, 22, 30
Middle two: 15 and 18
Median = (15 + 18) ÷ 2 = 16.5

Mode

The mode is the value that appears most often. Here 15 appears twice and every other number once, so the mode is 15. If every value is different there is no mode, and if two values tie there are two.

Range and spread

The range is the largest minus the smallest: 30 − 12 = 18. Standard deviation measures how far values typically sit from the mean. For this list it is about 5.93 if the numbers are the whole population and about 6.50 if they are a sample from a larger group. Use the sample version when your data is a subset.

Which average should you use?

• Use the mean for symmetric data without extreme values, such as test scores in a class.
• Use the median when a few extreme values would pull the mean away from what is typical, such as incomes or house prices.
• Use the mode for categories or the most common choice, such as the most popular shirt size.

Common mistakes

• Reporting the mean of skewed data as "typical".
• Forgetting to sort before finding the median.
• Averaging averages of groups of different sizes. Use a weighted average instead.

Paste your numbers into the average calculator to get all of these at once.

Try it yourself

1. Find the mean, median and mode of 6, 9, 9, 12, 14.
2. Four numbers are 18, 22, 19 and 25. What fifth number makes the mean 20?
3. Add 100 to the list in question 1. What happens to the mean and the median?

Answers: (1) Mean 10, median 9, mode 9; (2) 16 (the total must be 100, and the four numbers add to 84); (3) The mean jumps to 25, while the median only moves to 10.5.