Are the median and mean the same?

Although both describe aspects of the 'centre' of a distribution, they are not the same and can occasionally have very different values. This page describes some differences between the interpretation and properties of the median and mean.

Social versus economic indicator

For some data sets, the median can be considered to be a social indicator, whereas the mean can be interpreted as an economic indicator. For example, if a batch of values consists of the salaries of all teachers in a high school:

Outliers

An outlier has little effect on the numerical value of the median, whereas an outlier affects the mean more strongly. The median is therefore called a more robust measure of centre than the mean.

The distribution of values in the data set below is fairly symmetric, so the mean and median are similar.

Drag the cross for one of the larger values with the mouse towards the right of the axis (approx 90) and observe the effect on the mean and median.

You should observe that the median remains unchanged at 24, but the mean increases considerably. If this change had been caused by incorrect recording of the value, the resulting outlier would therefore have badly effected the mean, but not the median.

Skew distributions

When the distribution of a batch of values is fairly symmetrical, the mean and median are similar. However if the distribution is skew, then the mean is usually further into the tail of the distribution than the median.

This can be readily understood in relation to the balance interpretation of the mean — values far from the 'centre' have relatively high leverage, so the point of balance (the mean) is further into the tail of the distribution.

The diagram below shows the mean and median for a skew data set. Note that the mean is larger than the median (i.e. further into the tail).

You may drag crosses in the plot to investigate distributions for which the mean and median are most similar and dissimilar.