Mean, median and mode explained

The mean adds all the values and divides by how many there are. The median is the middle value once the data is sorted. The mode is the value that appears most often.

For 2, 3, 3, 5, 7, 10 the mean is 30 ÷ 6 = 5, the median is the average of 3 and 5, which is 4, and the mode is 3.

Add one extreme value, 100, to the same list. The mean jumps to about 18.6, while the median only moves to 5. The mean is pulled by extremes; the median is not.

That is why reports on incomes and house prices usually quote the median.

Use the mean for data that is fairly evenly spread, such as test scores in a class. Use the median when a few values are very large or small. Use the mode for categories or the most common size or choice, like the most popular shoe size.

A data set can have several modes, or none if every value is different.

The range, the difference between the largest and smallest values, shows how spread out the data is. Report it alongside the average, since two groups can share a mean and still look very different.

Our average calculator gives the mean, median, mode, range, sum and count for any list you paste in.