Blogging on Employment and Job Markets in US Metro Areas

Mean vs Median

Mean or median, which should we pay more attention to? First, for some background, the difference between the mean and median:

The mean is the average, the result of dividing the sum of two or more values by the number of values. So for three values, X, Y, and Z, the mean is (X+Y+Z)/3.

The median is the middle value in a set of values sorted in ascending or descending order. If the sample contains an even number of values, the median is defined as the mean of the middle two. To use X, Y, and Z again, if X > Y and Y > Z, then the median will be Y. No matter how many values we have, the median will be middle point of the dataset, with half of the remaining values above the median and the other half of the remaining values below the median.

As an example, lets look at a hypothetical sample of seven salaries for statisticians in a given city. From lowest to highest the salaries are:

$72,000  $75,000  $78,000  $82,000  $85,000  $88,000  $96,000

The mean, or average, of these salaries is $82,286, while the median is the middle value, $82,000. In this case the mean and median differ by only a small amount, so one may be tempted to conclude that we can use them interchangeably. However, the mean and median will not always be so close.

In many real-world situations, such as with salaries or house prices, the mean and the median often differ substantially. This is due to outliers, abnormally low or high values, which have a greater effect on the mean than the median. To illustrate this, let’s add a substantially higher salary to list above, an eighth statistician who has a salary of $145,000. Maybe this statistician is a manager, or for some other reason receives a much higher salary than the other statisticians in our sample. In any case, the average of these eight salaries is $90,125. The median of these eight salaries is $83,500. So with the addition of one outlier, the average has increased dramatically (by $7,839, or 9.5%) while the median’s increase is much smaller (by $1,500, or 1.8%). And this why the median is more often cited than the mean or average when comparing salaries or house prices among cities or over time: outliers or abnormal values have much less impact on the median.