Expectation is the center of gravity of a probability histogram, and is thus a measure of where the histogram is located on the number line. But histograms of very different distributions can have the same expectation.

In the example below, both Distribution 1 and Distribution 2 balance at 3.5.

The probabilities in Distribution 2 are more concentrated around the center of the distribution. So it seems *less spread out* than Distribution 1.

In this chapter we will quantify the spread or variability in a distribution. Once we have defined a measure of spread and examined how to calculate it, we will see what it tells us about the *tails* of the distribution, that is, probabilities of values that are far away from the expectation.