Median

A median is a statistical average. It denotes the average effective mid-value of a series of figures.

Example: You roll a six-sided die five times and it lands on these numbers, arranged by size: 1, 1, 2, 5, 6. The median of these five numbers is 2. It shows that half of the rolls gave you two or more points per roll, and that the other half gave you two points or less.

The median is not to be confused with the arithmetic mean. The latter is found by adding up the figures in a series and then dividing the sum by the number of figures. For the dice example above, you would calculate the arithmetic mean like this:

(1+1+2+5+6)/5=3

In this example, the arithmetic mean shows that you averaged 3 points per roll.

The advantage of a median over an arithmetic mean is that exceptionally high or low figures in a series do not impact the result as strongly. In the above example, the two high rolls of 5 and 6 points push the arithmetic mean up to 3 points. But in practice, half of the rolls were worth 2 points or less.

When the term average is used, it normally refers to the arithmetic mean. The median is used in specific cases. For example, salary statistics are often shown as medians because exceptionally high or low salaries skew the arithmetic mean (often upwards, as is the case when high managerial salaries are accounted for). A median salary shows that half of all employees included in the statistic earn that amount or more.

If the number of figures in the series (the number or rolls of the die, in the above example) is even, it is common to use the arithmetic mean to calculate the median. This is done by adding the two figures in the middle and dividing them by two.

Example: You roll a six-sided die six times and it lands on these points, arranged by size: 1, 1, 2, 3, 5, 6. The two middle figures are 2 and 3. So the median is calculated like this:

(2+3)/2=2.5

In this example, the median is 2.5, meaning that half of the rolls were higher than 2.5 points and the other half were lower than 2.5 points.