## 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 Variability

#### Range

The range is the simplest measure of variability to calculate, and one you have probably encountered many times in your life. The range is simply the highest score minus the lowest score. Let's take a few examples. What is the range of the following group of numbers: $\mathrm{10, \, 2, \, 5, \, 6, \, 7, \, 3, \, 4}$? Well, the highest number is $\mathrm{10}$, and the lowest number is $\mathrm{2}$, so $\mathrm{10 - 2 = 8}$. The range is $\mathrm{8}$. Let's take another example. Here's a dataset with $\mathrm{10}$ numbers: $\mathrm{99, \, 45, \, 23, \, 67, \, 45, \, 91, \, 82, \, 78, \, 62, \, 51}$. What is the range? The highest number is $\mathrm{99}$ and the lowest number is $\mathrm{23}$, so $\mathrm{99 - 23}$ equals $\mathrm{76}$; the range is $\mathrm{76}$. Now consider the two quizzes shown in Figure 1. On Quiz 1, the lowest score is $\mathrm{5}$ and the highest score is $\mathrm{9}$. Therefore, the range is $\mathrm{4}$. The range on Quiz 2 was larger: the lowest score was $\mathrm{4}$ and the highest score was $10$. Therefore the range is $\mathrm{6}$.