31. #37U.S. Population The estimated distribution (in millions) of the U.S. population by age for the year 2006 is shown in the circle graph. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard deviation of the data set. Use 70 as the midpoint for \"65 years and over.\" (Source: U.S. Census Bureau) Figure for Exercise 37 Figure for Exercise 38 31. #38Japan's Population Japan's estimated population for the year 2010 is given in the bar graph. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard deviation of the data set. (Source: U.S. Census Bureau, International Data Base) Extending the Basics 39. Coefficient of Variation The coefficient of variation CV describes the standard deviation as a percent of the mean. Because it has no units, you can use the coefficient of variation to compare data with different units. The following data show the heights (in inches) and weights (in pounds) of the members of a basketball team. Find the coefficient of variation for each data set. What can you conclude? Heights: 72 74 68 76 74 69 72 79 70 69 77 73 Weights: 180 168 225 201 189 192 197 162 174 171 185 210 39. Shortcut Formula You used SS x = S(x - x )2 when calculating variance and standard deviation. An alternate formula that is sometimes more convenient for hand calculations is You can find the sample variance by dividing the sum of squares by n - 1, and the sample standard deviation by finding the square root of the sample variance. a. Use the shortcut formula to calculate the sample standard deviation for the data set given in Exercise 19. b. Compare your results to those obtained in Exercise 19