104 Chapter 3 Numerical Summaries of Data 64. Exception to the skewness rule: Consider the following data set: 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 2 2 2 3 a. Compute the mean and median. b. Based on the mean and median, would you expect the data set to be skewed to the left, skewed to the right, or approximately symmetric? Explain. c. Construct a frequency histogram. Does the histogram have the shape you expected? Answers to Check Your Understanding Exercises for Section 3.1 1. Mean is 65.4; median is 60. 2. Mean is 68.5; median is 74.5. 3. The mean does not have to be a value that could possibly appear in the data set. 4. Skewed to the right 5. Skewed to the left 6. a. 1 b. 4 and 6 c. No mode SECTION 3.2 Measures of Spread Objectives 1. Compute the range of a data set 2. Compute the variance of a population and a sample 3. Compute the standard deviation of a population and a sample 4. Approximate the standard deviation with grouped data 5. Use the Empirical Rule to summarize data that are unimodal and approximately symmetric 6. Use Chebyshev’s Inequality to describe a data set 7. Compute the coefficient of variation Would you rather live in San Francisco or St. Louis? If you had to choose between these two cities, one factor you might consider is the weather. Table 3.3 presents the average monthly temperatures, in degrees Fahrenheit, for both cities. Table 3.3 Temperatures in San Francisco and St. Louis Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec San Francisco 51 54 55 56 58 60 60 61 63 62 58 52 St. Louis 30 35 44 57 66 75 79 78 70 59 45 35 Source: National Weather Service To compare the temperatures, we will compute their means. Mean for San Francisco = 51+54+55+56+58+60+60+61+63+62+58+52 12 = 57.5 Mean for St. Louis = 30+35+44+57+66+75+79+78+70+59+45+35 12 = 56.1 The means are similar: 57.5◦ for San Francisco and 56.1◦ for St. Louis. Does this mean that the temperatures are similar in both cities? Definitely not. St. Louis has a cold winter and a hot summer, while the temperature in San Francisco is much the same all year round.
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