Mean vs. Median

We now have two candidates to help us identify a typical value or the center of our data. Which is better? Which should we use? Neither is necessarily the best for all situations. In this section, we explore the relative strengths and weaknesses of the median and the mean.

Resistance to Extreme Data Values. Extreme data values are atypical and do not help us identify the center or typical values. Therefore we would like our estimate of the center not to be too affected by extreme data values.

An example from Gould's (1996) eloquent comparison of the median and the mean illustrates their differing resistance to extreme data values. In Gould's example there are five children, one has a penny, one a dime, another a quarter, one a dollar, and the last one ten dollars. Use the graphs below to find the median (left) and the mean (right) amounts of money these children have.

Median
Mean

Which estimate of the center, the median or the mean, seems more representative of the amount of money the "typical" child has in this group?

The median is 25 cents (rounded to 30 cents in the graph) and seems fairly typical for all the but the largest amount. The kid in this group with ten dollars just isn't typical. The median is not affected by the extreme value of ten dollars. The mean is $2.27 (rounded to $2.30 in the graph) and doesn't seem representative of any of the amounts. The mean is considerably higher (by at least $1.27) than all but the most extreme amount and it isn't very close to the exteme amount. In short, the mean does not represent any of the money amounts very well.

Lesson: When there are a few extreme observations, the mean may provide a very poor estimate of the center of the data. The median, however, remains in the center of the bulk of the data values and is therefore still a typical value. Thus, the median is more resistant to extreme values than the mean and is therefore preferred for data where there might be a few extreme values, especially on one side of the center.