# Question

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 (1,000s of 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 representative of the distance traveled by one of the 191 buses? Explain your answer.

Distance Traveled (1,000s of 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 representative of the distance traveled by one of the 191 buses? Explain your answer.

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