Mean, median and mode explained
- Mean (average): add the numbers and divide by how many there are.
- Median: the middle value when the numbers are sorted. With an even count, it is the average of the two middle values.
- Mode: the value that appears most often. A list can have no mode or several.
- Range: largest minus smallest.
Worked example
12, 15, 11, 15, 18, 20, 15, 9 sorted: 9, 11, 12, 15, 15, 15, 18, 20.
- Mean: 115 ÷ 8 = 14.375
- Median: (15 + 15) ÷ 2 = 15
- Mode: 15 (three times)
- Range: 20 − 9 = 11
Which average should you use?
The mean uses every value but is pulled by outliers; the median is better for skewed data such as incomes or house prices. The mode suits categories (the most common shoe size).
Worked example
For 3, 7, 7, 2, 9: sort them (2, 3, 7, 7, 9). The mean is 28 ÷ 5 = 5.6, the median is the middle value, 7, and the mode is 7 because it appears most often. The range is 9 − 2 = 7.
Even number of values
With an even count, the median is the average of the two middle numbers. For 2, 3, 7, 9 it is (3 + 7) ÷ 2 = 5.
Which average to use
The mean is pulled by extreme values, so incomes and house prices are usually reported with the median. The mode is best for categories, like the most common shoe size.
Related calculators
- Standard Deviation Calculator: Sample or population SD and variance.
- Percentage Calculator: X% of Y, X is what % of Y, and more.
- Rounding Calculator: Round to decimals, tens or significant figures.
Questions people ask
How do I find the median of an even set of numbers?
Sort the numbers and average the two in the middle. For 3, 5, 8, 10 the median is (5 + 8) ÷ 2 = 6.5.
What if no number repeats?
Then there is no mode. If two values tie for most frequent, the list is bimodal and both are modes.
Formula checked October 2026 · How we calculate