Solo Biz Soft Editorial Team Mean, median and mode are three ways to describe the middle of a set of numbers. Each tells you something different. This guide explains how to calculate each and when to use it.
The formula
Mean = sum of values ÷ number of values. Median = the middle value of the sorted list (or the average of the two middle values). Mode = the value that appears most often.
Step by step
- Write the numbers in order, smallest to largest.
- Add them up and divide by how many there are to find the mean.
- Find the middle number for the median. With an even count, average the two middle numbers.
- Find the number that appears most often for the mode.
Worked example
For 12, 15, 18, 15, 20, 9: sorted, they are 9, 12, 15, 15, 18, 20. The sum is 89 and the mean is 14.83. The median is (15 + 15) ÷ 2 = 15. The mode is 15. The range is 20 − 9 = 11.
Common mistakes
- Forgetting to sort before finding the median
- Using the mean when a few extreme values distort it
- Assuming there is always a single mode
Skip the maths: use our free average calculator. For exam results, try the GPA calculator.
Frequently asked questions
When should I use the median instead of the mean?
When extreme values could distort the mean, as with incomes or house prices.
Can there be no mode?
Yes, if every value appears once.
What is a weighted average?
An average where some values count more than others, such as credits in a GPA.
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This article is general information only.