Question

The median and mean of a set of data can often time be quite different from one another. One example of this is household income in the United States. According to the U.S. Census Bureau’s 2014 Annual Social and Economic Supplement, mean household income in 2014 was $72, 641, while median household income was $51,939.

Why are the mean and median so different in this case? Find another example of a statistic in which the mean and median values would be expected to be quite different and explain the difference.

Answer 1

When the distribution is skewed to right the mean will pull upward. That is for right skewed distribution mean will be greater than median.

In the given case, some household income are much larger than most of household incomes. So distribution of household income will be skewed to right. Therefore mean is greater than median.

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Other example can be salaries of employees in a company. Some employees like director, CEO etc of the company must be very highly paid.

So distribution of salary will be skewed to right and will have mean greater than median.