Practical guide

Average, mean and median: how to choose the right measure

“Average” often means arithmetic mean, but the median can describe a typical value better when a data set contains extreme numbers. This guide shows the difference with calculations you can reproduce.

What does “average” usually mean?

In everyday arithmetic, average usually refers to the arithmetic mean. Add all values and divide the total by the number of values. For 12, 18, 14, 20 and 16, the sum is 80. There are five values, so the mean is 80 ÷ 5 = 16.

This method uses every number in the list. That makes it useful for school scores, repeated measurements, simple budgets and many other cases where each value should contribute equally.

How the median is different

The median is the middle value after the numbers are sorted. For 12, 14, 16, 18 and 20, the median is 16. When the list contains an even number of values, average the two values in the center.

The median becomes especially useful when one or two values are unusually high or low. Imagine monthly repair costs of 20, 25, 30, 35 and 900 dollars. The mean is 202 dollars, but the median is 30 dollars. Both answers are mathematically correct; they answer different questions.

Mean or median: which one should you report?

Use the mean when every observation should affect the result and the data are reasonably balanced. Use the median when you want the center of an ordered list and outliers could distort the mean. In a report, it can be useful to show both rather than choosing only one.

Worked example

Suppose five delivery times are 42, 45, 47, 50 and 86 minutes. The mean is (42 + 45 + 47 + 50 + 86) ÷ 5 = 54 minutes. The median is 47 minutes. The unusually long 86-minute trip pulls the mean upward, while the median stays at the central observation.

What the range adds

The range is maximum minus minimum. In the delivery example, 86 − 42 = 44 minutes. A mean of 54 minutes tells you the center of the values, while the 44-minute range warns that the observations are spread out. Two data sets can have the same mean and very different ranges.

Common mistakes

• Dividing by the wrong number of observations.
• Confusing the median with the midpoint between the minimum and maximum.
• Using the mean for strongly skewed data without checking outliers.
• Rounding too early and carrying the rounding error into later calculations.

Try the values yourself

Use the Average Calculator to paste a list and compare mean, median, sum, count, minimum, maximum and range at the same time.