How to find the mean, median and mode of numbers

Steps

1. Write the numbers in a list and count them. Here there are 5: 12, 18, 24, 30, 36.
2. Add them up: 120. Divide by the count to get the mean: 120 ÷ 5 = 24.
3. Sort them from smallest to largest and pick the middle one for the median: 24.
4. If the count is even, take the average of the two middle numbers.
5. For the mode, find the value that appears most often. If none repeats, there is no mode.

An example with an even count and a mode

Take 4, 8, 8, 10, 15, 20. The sum is 65 and there are 6 numbers, so the mean is 10.83. Sorted, the two middle numbers are 8 and 10, so the median is 9. The value 8 appears twice, so the mode is 8.

The three answers differ because the list is not symmetric: the large value, 20, pulls the mean above the median.

Which one to use

Use the mean when the values are fairly even, such as test scores. Use the median when a few extreme values would distort the mean, such as salaries or house prices. Use the mode for the most common choice, such as the most popular shoe size. A list can have more than one mode if two values tie.

Spread as well as the middle

The range, the largest minus the smallest, shows how spread out the numbers are. For 40, 55, 62, 70 and 90 the sum is 317, the mean 63.4, the median 62 and the range 50. Two sets can share a mean and still be very different, so look at the range or the individual values too.