Exercise 2 Page 720

Our goal is to explain why we use the median, not the mean, to describe the center of a non-symmetric distribution. To do so, let's remember all we know about symmetric and non-symmetric distributions.

Symmetric Distribution

In a symmetric distribution, data are distributed evenly around the mean.

In general, if the left side of the distribution looks like the right side, then we are dealing with symmetric distribution.

Non-symmetric Distribution

Not all data sets have a symmetric distribution. If one side of the distribution is taller, then the data set is skewed.

In general, there are two types of non-symmetric distributions. We can see the difference between all the mentioned types of distribution in the following applet. Notice that the mean and median are roughly the same in symmetric distribution. This is not true for non-symmetric distributions. Also, in a skew distribution the median will always fall farther from the tail. This is because it is less affected by the outliers.

Mean vs Median

When we describe the center of a non-symmetric distribution, we usually use the median. We prefer the median because it is less affected by outliers — the mean will always fall in the direction of the tail of the distribution.