The mean vs. median are both measures of central tendency, but they summarize data in different ways and respond differently to outliers and skewed distributions.
- The mean is the arithmetic average. You calculate it by adding all the values and dividing by the number of values.
- The median is the middle value when the data are ordered from smallest to largest. If the number of values is even, the median is the average of the two middle values.
Mean vs. Median Key Differences
The mean is sensitive to extreme values. A single unusually high or low number can pull it away from the center of the rest of the data. In contrast, the median is resistant to outliers and provides a better sense of the “typical” value when the data are skewed.
In symmetric distributions, the mean and median are usually close or identical. But in skewed distributions, they diverge. In a skewed distribution, extreme values in the longer tail pull the mean away from the center more than the median.
Hence, a right-skewed distribution has a mean greater than the median. Conversely, a left-skewed distribution has a mean less than the median. This relationship makes the difference between the mean and median a useful clue about the shape of a distribution.
For example, in the graph below, the gap between the mean and median exceeds $9,000. Because of the skew, the median offers a more accurate summary of the data’s central tendency.
When to Use Each
The choice between mean and median depends on the characteristics of the data. Consider the following general guidance:
- Use the mean when your data are symmetrical and free from extreme outliers.
- Use the median when your data are skewed or contain extreme values that could distort the mean.
Mean vs. Median Example
Suppose five people have salaries of $45,000, $47,000, $50,000, $51,000, and $1,000,000.
The mean salary is $238,600. However, a single extremely high value pulls that number far above the typical income. It’s the average but it doesn’t represent what most people actually make.
The median salary, on the other hand, is $50,000. This value better reflects what most people in the group earn. In this case, the median gives a much more accurate picture of the group’s central tendency than the mean.
« Back to Glossary Index