solution: Both the stemplot and the histogram show symmetric, bell-shaped distributions. The
graph is symmetric and centered about 66 inches. In the histogram, the boundaries of the bars
are 59 ≤ x < 61, 61 ≤ x < 63, 63 ≤ x < 65, ..., 71 ≤ x < 73. Note that for each interval, the
lower bound is contained in the interval, while the upper bound is part of the next larger
interval. Also note that the stemplot and the histogram convey the same visual image for the
shape of the data.Measures of Center
In the last example of the previous section, we said that the graph appeared to be centered about a height
of 66′′. In this section, we talk about ways to describe the center of a distribution. There are two primary
measures of center: the mean and the median . There is a third measure, the mode , but it tells where the
most frequent values occur more than it describes the center. In some distributions, the mean, median, and
mode will be close in value, but the mode can appear at any point in the distribution.
Mean
Let x (^) i represent any value in a set of n values (i = 1, 2, ..., n ). The mean of the set is defined as the sum
of the x ’s divided by n . Symbolically, . Usually, the indices on the summation symbol in the
numerator are left out and the expression is simplified to . Σ x means “the sum of x ” and is
defined as follows: = x 1 + x 2 + ... + xn . Think of it as the “add-’em-up” symbol to help remember
what it means. is used for a mean based on a sample (a statistic ). In the event that you have access to
an entire distribution (such as in Chapters 9 and 10 ), its mean is symbolized by the Greek letter μ .
(Note: In the previous chapter, we made a distinction between statistics , which are values that
describe sample data, and parameters , which are values that describe populations. Unless we are clear