Question

Sometimes the mean is poor indicator of a distribution's location and median is used instead. One instance of this situation is reporting salaries as a description of economic well-being: the median is usually reported instead of the mean. Why do you think this is the case? What shape do you think the distribution of salaries takes? Where do outliers occur in such a distribution?

Answer 1

The mean value is affected very much by extream values. In the case of extreme items, mean gives a distorted picture of the distribution and no longer remains representative of the distribution. Also, in extremely asymmetrical (skewed) distribution, usually mean is not a suitable measure of location because the tails have extreme values. Whereas, the median is not at all affected by extreme values.

Here, the given variable salary is generally a positive skewness data. It has extreme values of some of the high salary jobs. Therefore, the median is usually reported instead of the mean for salary variables dues to its unaffected by extreme values. The shape of the salary variable will be positive skewness. The outliers occur at the right of the distribution (right tail).