## Numerical Measures of Central Tendency and Variability

Read these sections and complete the questions at the end of each section. First, we will define central tendency and introduce mean, median, and mode. We will then elaborate on median and mean and discusses their strengths and weaknesses in measuring central tendency. Finally, we'll address variability, range, interquartile range, variance, and the standard deviation.

### Measures of Central Tendency

#### Median

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.