The mean and the median are two different ways to describe the center of a data set. Sometimes they're equal. Sometimes they're very different. Looking at both side-by-side tells us about the shape of the distribution.

To compute the mean: add all the values, then divide by the number of values.

To compute the median: order the values from least to greatest, then find the middle (or average the two middle values for even N).

Symmetric example: The data set 4, 6, 8, 6, 6 has mean (4 + 6 + 8 + 6 + 6) / 5 = 30 / 5 = 6. Sorted: 4, 6, 6, 6, 8. The median is the 3rd value, 6. Mean = median = 6.

Skewed-right example: The data set 2, 3, 4, 5, 21 has mean (2 + 3 + 4 + 5 + 21) / 5 = 35 / 5 = 7. Sorted: 2, 3, 4, 5, 21. The median is 4. The mean (7) is much greater than the median (4) because the value 21 pulls the mean up. The median is not affected the same way.

The pattern:

• When a data set is roughly symmetric (no extreme values), mean ≈ median.
• When a data set has a value that's much greater than the others, the mean is pulled up and is greater than the median.
• When a data set has a value that's much smaller than the others, the mean is pulled down and is less than the median.