What is the difference between median and mean?

1 Answer

See below:


Let's look at the numbers 1, 2, 3, 4, 5.

The mean is the sum of the values divided by the count:


The median is the middle term when listed in ascending (or descending!) order, which is 3.

So in this case they are equal.

The mean and the median will react differently to different changes to the data set. For instance, if I change the 5 to a 15, the mean will definitely change #(25/5=5)# but the median will stay the same at 3.

If the dataset changes where the sum of the values is 15 but the middle term changes, the median will move but the mean will stay put:

#1,1,2,3,8# - the mean is 3 but the median is 2.

This shows why, when dealing with large data sets, different measures of the centre are used to help better describe the data.