Mean, median and mode explained
All three are ways to describe the "middle" or typical value of a set of numbers, and each answers a slightly different question.
- Mean (average) — add all values and divide by how many there are. It uses every number, so one extreme value pulls it strongly.
- Median — sort the values and take the one in the middle. With an even count, average the two middle values. Extreme values barely affect it.
- Mode — the value that appears most often. A list can have one mode, several, or none if every value is different.
- Range — the largest value minus the smallest, a quick measure of spread. For a better one, use the standard deviation calculator.
Worked example
Take the list 2, 4, 4, 4, 5, 5, 7, 9 (8 values).
- Mean: 2 + 4 + 4 + 4 + 5 + 5 + 7 + 9 = 40; 40 ÷ 8 = 5.
- Median: the list is already sorted; the 4th and 5th values are 4 and 5, so the median is (4 + 5) ÷ 2 = 4.5.
- Mode: 4 appears three times, more than any other value, so the mode is 4.
- Range: 9 − 2 = 7.
Which average should you use?
Use the mean for values that are spread fairly evenly, such as test scores in a class or daily temperatures. Use the median when a few values are far from the rest — incomes and house prices are usually reported as medians because a handful of very high values would make the mean misleading. Use the mode for categories or repeated values, like the most common shoe size sold.
Example: five salaries of 40, 42, 45, 48 and 300 thousand. The mean is 95 thousand, which describes nobody; the median of 45 thousand is far more typical.
Weighted averages and the geometric mean
If some values count more than others — exam components or course credits — you need a weighted average; the grade calculator and GPA calculator handle those. The geometric mean (shown when all numbers are positive) is the right average for growth rates: returns of +10% and −10% average to a growth factor of √(1.1 × 0.9) ≈ 0.995, a small loss, not zero.
Frequently asked questions
How do I calculate the average of numbers?
Add them all together and divide by how many numbers there are. The average of 6, 8 and 13 is (6 + 8 + 13) ÷ 3 = 9.
How do I find the median of an even number of values?
Sort the values and average the two in the middle. For 3, 5, 8, 10 the middle values are 5 and 8, so the median is 6.5.
Can there be more than one mode?
Yes. If two or more values share the highest count, the set is bimodal or multimodal and every one of them is a mode. If all values appear once, there is no mode.
What is the difference between mean and average?
In everyday use they are the same thing: the arithmetic mean. "Average" is sometimes used loosely for the median or mode too, so statisticians prefer the specific terms.
Last updated: October 9, 2026