Question

Compared to others, which one of the following is not robust to outliers? a) Mean b) Median c) Mode d) 50th percentile

Answer 1

The mean.

Explanation:

The mean is not robust.

The presence of an outlier greatly affects the value of a mean.

An example will illustrate this.

Find the mean of the numbers 2 3 5 6 34.

34 is an outlier. The mean = (2+3+5+6+34) / 5 = 10.

Now if we replace the outlier with a number closer to the others:

Say we have 2 3 5 6 8 :

The mean = (2+3+5+6+8) / 5 = 4.8 which is a much truer measure of centrality than 10.