The mean, also called the average, is a statistic that provides information about the center of a distribution. If we measured the heights of 10-year-old and of 18-year-old boys, then plotted a frequency distribution for each group, we would find that both distributions are normal, but the two distributions would be centered at different heights, and this difference would be indicated by their different means (Figure 17.8).

Suppose that we have five measurements of height in centimeters: 160, 161, 167, 164, and 165. If we represent a group of measurements as x₁, x₂, x₃, and so forth, then the mean (x̄) is calculated by adding all the individual measurements and dividing by the total number of measurements in the sample (n):

In our example, x₁ = 160, x₂ = 161, x₃ = 167, and so forth. The mean height x̄ equals

A shorthand way to represent this formula is

or

where the symbol Σ means “the summation of” and x_i represents the individual x values.