EXAMPLE 1.31 Mean and Median

Figure 1.19 illustrates this fact about the mean. A symmetric curve balances at its center because the two sides are identical. The mean and median of a symmetric density curve are equal, as in Figure 1.18(a). We know that the mean of a skewed distribution is pulled toward the long tail. Figure 1.18(b) shows how the mean of a skewed density curve is pulled toward the long tail more than is the median. It is hard to locate the balance point by eye on a skewed curve. There are mathematical ways of calculating the mean for any density curve, so we are able to mark the mean as well as the median in Figure 1.18(b).