Numerical Measures of Central Tendency and Variability

The median is also a frequently used measure of central tendency. The median is the midpoint of a distribution: the same number of scores is above the median as below it. For the data in Table 1, there are $31$ scores. The 16th highest score (which equals $20$) is the median because there are $15$ scores below the $\mathrm{16th}$ score and $15$ scores above the $\mathrm{16th}$ score. The median can also be thought of as the $\mathrm{50th}$ percentile.

Computation of the Median

When there is an odd number of numbers, the median is simply the middle number. For example, the median of $2$, $4$, and $7$ is $4$. When there is an even number of numbers, the median is the mean of the two middle numbers. Thus, the median of the numbers $2,4,7,12$ is $(4+7) / 2=5.5$. When there are numbers with the same values, then the formula for the third definition of the $\mathrm{50th}$ percentile should be used.