Why do you think the Empirical Rule and your percentages do not match well? Edu.

Brand Price per Roll Number of Sheets per Roll Cost per Sheet 7 0.79 52 .0152 8 0.75 72 .0104 9 0.72 80 .0090 10 0.53 52 .0102 11 0.59 85 .0069 12 0.89 80 .0111 13 0.67 85 .0079 14 0.66 80 .0083 15 0.59 80 .0074 16 0.76 80 .0095 17 0.85 85 .0100 18 0.59 85 .0069 19 0.57 78 .0073 20 1.78 180 .0099 21 1.98 180 .0011 22 0.67 100 .0067 23 0.79 100 .0079 24 0.55 90 .0061 a. Compute the standard deviation for both the price per roll and the price per sheet. b. Which is more variable, price per roll or price per sheet? c. In your comparison in part b, should you use s or CV? Justify your answer. 3.46 Refer to Exercise 3.45. Use a scatterplot to plot the price per roll and number of sheets per roll. a. Do the 24 points appear to fall on a straight line? b. If not, is there any other relation between the two prices?

c. What factors may explain why the ratio of price per roll to number of sheets is not

a constant? 3.47 Construct boxplots for both price per roll and number of sheets per roll. Are there any “unusual” brands in the data? Env. 3.48 The paper “Conditional simulation of waste-site performance” [Technometrics 1994 36: 129 –161] discusses the evaluation of a pilot facility for demonstrating the safe management, storage, and disposal of defense-generated, radioactive, transuranic waste. Researchers have determined that one potential pathway for release of radionuclides is through contaminant transport in ground- water. Recent focus has been on the analysis of transmissivity, a function of the properties and the thickness of an aquifer that reflects the rate at which water is transmitted through the aquifer. The following table contains 41 measurements of transmissivity, T, made at the pilot facility. 9.354 6.302 24.609 10.093 0.939 354.81 15399.27 88.17 1253.43 0.75 312.10 1.94 3.28 1.32 7.68 2.31 16.69 2772.68 0.92 10.75 0.000753 1.08 741.99 3.23 6.45 2.69 3.98 2876.07 12201.13 4273.66 207.06 2.50 2.80 5.05 3.01 462.38 5515.69 118.28 10752.27 956.97 20.43 a. Draw a relative frequency histogram for the 41 values of T. b. Describe the shape of the histogram.

c. When the relative frequency histogram is highly skewed to the right, the Empirical

Rule may not yield very accurate results. Verify this statement for the data given.

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

tograms. A transformation of the data will sometimes achieve this shape. Replace the given 41 T values with the logarithm base 10 of the values and reconstruct the relative frequency histogram. Is the shape more mound-shaped than the original data? Apply 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