Demo: The Effects of the Mean and the Median on Outliers

Example 1:

Here is a picture of a data set where all of the points are less than 2. Notice that the mean and the median are the same.

Now, I am going to add a point near 3.5.

When this point is added, the mean got pulled in the direction of the outlier. The mean got larger. However, the median stayed relatively the same.

Example 2

Let’s see what happens, if we add an outlier in the opposite direction. So, we start off with a data set with the points about 3.4. Notice that once again the mean and the median are almost the same.

Now, let’s add a point around 2.

After this point was added, the mean got much smaller, but the median really didn’t change much.

Conclusion:

The mean is highly influenced by outliers; in fact, the mean is pulled in direction of the outlier.

The median is not highly influenced by outliers. It is said to be resistant.