Compare Mean and Median Under an Outlier

Compare Mean and Median

When a data set has an outlier, the mean and median can behave differently. The mean uses every value, so one very large or very small number can pull it toward that extreme. The median is the middle value after the data are ordered, so it is usually less affected by an outlier.

Method

1. Order the data from least to greatest.
2. Find the median:
   • If there is an odd number of values, the median is the middle one.
   • If there is an even number of values, the median is the average of the two middle values.
3. Find the mean by adding all values and dividing by the number of values.
4. Compare the results:
   • If there is an outlier, expect the mean to move more than the median.
   • State which measure is larger or smaller, or which one better represents the data.

Check your work

Make sure the data are ordered before finding the median, and recheck the sum used for the mean. If one value is far from the others, see whether it changed the mean a lot while leaving the median nearly the same.