Question

Explain when the median of a data set is a better
measure of center than the mean.
HELS

Answer 1

Sample Response: When there is an outlier in the data set, the dot plot or histogram will be skewed. In a skewed representation, the mean is pulled up or down toward the tail of the data. Therefore, skewed data affects the mean more than the median.

What did you include in your response? Check all that apply.

The dot plot or histogram will be skewed.

The mean is pulled up or down toward the tail.

The mean is affected more than the median.

Answer 2

A common used example is home prices. Many home price values are clustered together (say in the 50 thousand to 150 thousand range). However, there are very expensive outliers, such as million or multi-million dollar (celebrity) homes. Those few outliers pull on the arithmetic mean to make it larger than what the main cluster is centered around. So the mean is larger than it should be. What we could do is ignore those outliers or we can look at the median to get a better sense of what the center is. So that's why home prices often go with the median rather than the mean.