Right, and median is a much better measurement of the central tendency for income because median deals with outliers much better. Bill Gates isn’t going to skew the data when looking at the median. When things have few outliers, mean is better (and you’re right, mean and median will be close with large sets of normally distributed data). The biggest advantage to using mean with something like this is that changes in the data set will affect the mean, where it may not with the median.
Let’s say you have @EdFred’s magic driving scores and we have 11 drivers that score:
{1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 10}
Mean: 4.63
Median: 4
Now lets say they all attend @EdFred’s driving school. After attending the driving school, some of their scores went up. Obviously the worse drivers will show the bigger improvement.
After driving school, the scores are:
{2, 2, 2, 3, 4, 4, 6, 8, 8, 10, 10}
Mean: 5.36
Median: 4
So, almost everybody got better, which is reflected in the mean/average, but the median score stayed the same. That’s why for something like this (or GPA, etc.) median doesn’t show quite the story that the mean does.
Edit: Obviously I created a data set which proves my point, and other data sets may not, but the general theory still stands. Large data set with a normal-ish distribution and few outliers, mean is what you want. Discrete data set where you want to remove the effect of outliers, median is the way to go.
