Data analysts often find it easier to work with mound-shaped relative frequency his-

the Empirical Rule to the transformed data and verify that it yields more accurate results than it did with the original data. Soc. 3.49 A random sample of 90 standard metropolitan statistical areas SMSAs was studied to obtain information on murder rates. The murder rate number of murders per 100,000 people was recorded, and these data are summarized in the following frequency table. Class Interval f i Class Interval f i ⫺ .5 –1.5 2 13.5 –15.5 9 1.5 –3.5 18 15.5 –17.5 4 3.5 –5.5 15 17.5 –19.5 2 5.5 –7.5 13 19.5 –21.5 1 7.5 –9.5 9 21.5 –23.5 1 9.5 –11.5 8 23.5 –25.5 1 11.5 –13.5 7 Construct a relative frequency histogram for these data.

3.50 Refer to the data of Exercise 3.49. a. Compute the sample median and the mode.

b. Compute the sample mean. c. Which measure of central tendency would you use to describe the center of the distri- bution of murder rates?

3.51 Refer to the data of Exercise 3.49. a. Compute the interquartile range.

b. Compute the sample standard deviation. 3.52 Using the homeownership data in Exercise 3.11, construct a quantile plot for both years.

a. Find the 20th percentile for the homeownership percentage and interpret this value

for the 1996 data.

b. Congress wants to designate those states that have the highest homeownership percent-

age in 1996. Which states fall into the upper 10th percentile of homeownership rates?

c. Similarly identify those states that fall into the upper 10th percentile of homeownership

rates during 1985. Are these states different from the states in this group during 1996? Gov. 3.53 Per capita expenditure dollars for health and hospital services by state are shown here. Dollars f 45 –59 1 60 –74 4 75 – 89 9 90 –104 9 105 –119 12 120 –134 6 135 –149 4 150 –164 1 165 –179 3 180 –194 195 –209 1 Total 50 a. Construct a relative frequency histogram. b. Compute approximate values for and s from the grouped expenditure data. y Engin. 3.54 The Insurance Institute for Highway Safety published data on the total damage suffered by compact automobiles in a series of controlled, low-speed collisions. The data, in dollars, with brand names removed are as follows: 361 393 430 543 566 610 763 851 886 887 976 1,039 1,124 1,267 1,328 1,415 1,425 1,444 1,476 1,542 1,544 2,048 2,197 a. Draw a histogram of the data using six or seven categories. b. On the basis of the histogram, what would you guess the mean to be? c. Calculate the median and mean. d. What does the relation between the mean and median indicate about the shape of the data? Soc. 3.55 Data are collected on the weekly expenditures of a sample of urban households on food including restaurant expenditures. The data, obtained from diaries kept by each household, are grouped by number of members of the household. The expenditures are as follows: 1 member: 67 62 168 128 131 118 80 53 99 68 76 55 84 77 70 140 84 65 67 183 2 members: 129 116 122 70 141 102 120 75 114 81 106 95 94 98 85 81 67 69 119 105 94 94 92 3 members: 79 99 171 145 86 100 116 125 82 142 82 94 85 191 100 116 4 members: 139 251 93 155 158 114 108 111 106 99 132 62 129 91 5⫹ members: 121 128 129 140 206 111 104 109 135 136 a. Calculate the mean expenditure separately for each number of members. b. Calculate the median expenditure separately for each number of members. 3.56 Answer the following for the data in Exercise 3.55: a. Calculate the mean of the combined data, using the raw data. b. Can the combined mean be calculated from the means for each number of members? c. Calculate the median of the combined data using the raw data. d. Can the combined median be calculated from the medians for each number of members? Gov. 3.57 Federal authorities have destroyed considerable amounts of wild and cultivated marijuana plants. The following table shows the number of plants destroyed and the number of arrests for a 12-month period for 15 states. State Plants Arrests 1 110,010 280 2 256,000 460 3 665 6 4 367,000 66 5 4,700,000 15 6 4,500 8 7 247,000 36 8 300,200 300 9 3,100 9 10 1,250 4 11 3,900,200 14 12 68,100 185 13 450 5 14 2,600 4 15 205,844

33