Using your results from parts a and b, comment on the relative sensitivity of the

Gov. 3.24 Effective tax rates per 100 on residential property for three groups of large cities, ranked by residential property tax rate, are shown in the following table. Group 1 Rate Group 2 Rate Group 3 Rate Detroit, MI 4.10 Burlington, VT 1.76 Little Rock, AR 1.02 Milwaukee, WI 3.69 Manchester, NH 1.71 Albuquerque, NM 1.01 Newark, NJ 3.20 Fargo, ND 1.62 Denver, CO .94 Portland, OR 3.10 Portland ME 1.57 Las Vegas, NV .88 Des Moines, IA 2.97 Indianapolis, IN 1.57 Oklahoma City, OK .81 Baltimore, MD 2.64 Wilmington, DE 1.56 Casper, WY .70 Sioux Falls, IA 2.47 Bridgeport, CT 1.55 Birmingham, AL .70 Providence, RI 2.39 Chicago, IL 1.55 Phoenix, AZ .68 Philadelphia, PA 2.38 Houston, TX 1.53 Los Angeles, CA .64 Omaha, NE 2.29 Atlanta, GA 1.50 Honolulu, HI .59 Source: Government of the District of Columbia, Department of Finance and Revenue, Tax Rates and Tax Burdens in the District of Columbia: A Nationwide Comparison, annual. a. Compute the mean, median, and mode separately for the three groups. b. Compute the mean, median, and mode for the complete set of 30 measurements. c. What measure or measures best summarize the center of these distributions? Explain. 3.25 Refer to Exercise 3.24. Average the three group means, the three group medians, and the three group modes, and compare your results to those of part b. Comment on your findings.

3.5 Describing Data on a Single Variable: Measures of Variability

Engin. 3.26 Pushing economy and wheelchair-propulsion technique were examined for eight wheelchair racers on a motorized treadmill in a paper by Goosey and Campbell [Adapted Physical Activity Quarterly 1998 15:36 –50]. The eight racers had the following years of racing experience: Racing experience years: 6, 3, 10, 4, 4, 2, 4, 7

a. Verify that the mean years’ experience is 5 years. Does this value appear to ade-

quately represent the center of the data set?

b. Verify that c. Calculate the sample variance and standard deviation for the experience data.

How would you interpret the value of the standard deviation relative to the sample mean? 3.27 In the study described in Exercise 3.26, the researchers also recorded the ages of the eight racers. Age years: 39, 38, 31, 26, 18, 36, 20, 31 a. Calculate the sample standard deviation of the eight racers’ ages. b. Why would you expect the standard deviation of the racers’ ages to be larger than the standard deviation of their years of experience? Engin. 3.28 For the data in Exercise 3.26,

a. Calculate the coefficient of variation CV for both the racer’s age and their years of

experience. Are the two CVs relatively the same? Compare their relative sizes to the relative sizes of their standard deviations.

b. Estimate the standard deviations for both the racer’s age and their years of experience

by dividing the ranges by 4. How close are these estimates to the standard deviations calculated in Exercise 3.27? ai y ⫺ y 2 ⫽ ai y ⫺ 5 2 ⫽ 46.