Construct a relative frequency histogram plot for the homeownership data given in the

3.4 Describing Data on a Single Variable: Measures of Central Tendency

Basic 3.15 Compute the mean, median, and mode for the following data: 55 85 90 50 110 115 75 85 8 23 70 65 50 60 90 90 55 70 5 31 Basic 3.16 Refer to the data in Exercise 3.15 with the measurements 110 and 115 replaced by 345 and 467. Recompute the mean, median, and mode. Discuss the impact of these extreme measure- ments on the three measures of central tendency. Basic 3.17 Refer to the data in Exercise 3.15 and 3.16. Compute a 10 trimmed mean for both data sets—that is, the original and the one with the two extreme values. Do the extreme values affect the 10 trimmed mean? Would a 5 trimmed mean be affected by the two extreme values? Basic 3.18 Determine the mean, median, and mode for the data presented in the following frequency table. Class Interval Frequency 2.0 – 4.9 5 5.0 –7.9 13 8.0 –10.9 16 11.0 –13.9 9 14.0 –16.9 4 17.0 –19.9 2 20.0 –22.9 2 Engin. 3.19 A study of the reliability of buses [“Large sample simultaneous confidence intervals for the multinominal probabilities on transformations of the cell frequencies,” Technometrics 1980 22:588] examined the reliability of 191 buses. The distance traveled in 1,000s of miles prior to the first major motor failure was classified into intervals. A modified form of the table follows. Distance Traveled 1,000 miles Frequency 0 –20.0 6 20.1– 40.0 11 40.1– 60.0 16 60.1–100.0 59 100.1–120.0 46 120.1–140.0 33 140.1–160.0 16 160.1–200.0 4 a. Sketch the relative frequency histogram for the distance data and describe its shape. b. Estimate the mode, median, and mean for the distance traveled by the 191 buses.

c. What does the relationship among the three measures of center indicate about the

shape of the histogram for these data?

d. Which of the three measures would you recommend as the most appropriate repre-

sentative of the distance traveled by one of the 191 buses? Explain your answer. Med. 3.20 In a study of 1,329 American men reported in American Statistician [1974 28:115 –122] the men were classified by serum cholesterol and blood pressure. The group of 408 men who had