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 vs 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 employees in a company,
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 8.0) and observe the effect on the mean and median.
You should observe that the median remains unchanged at 2.4, 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.
Guinea pig survival
The diagram below shows the number of days that 72 guinea pigs survived after being injected with tubercle bacilli.
Since the data have a long tail of high survival times, the mean is further into the tail (i.e. larger) than the median.
Sunshine hours in Gaborone
In a study of the viability of solar cookers in Botswana, sunshine data from the years 1978 to 1997 were analysed. The following jittered dot plot shows the total sunshine hours on 25th February each year from 1978 to 1997.
In this data set, the data have a skew distribution with a long tail to the left so the mean daily hours of sunshine is much less than the median (but again further into the long tail of the distribution).