AP StatsName______
Measures of Center
1. The Highway Loss Data Institute publishes data on repair costs resulting from a 5-mph crash test of a car moving forward into a flat barrier. The following table gives data for 10 midsize luxury cars tested in October 2002. Compute the mean and the median. Do you think the mean or the median is more representative the data set? Explain.
2. The Highway Loss Data Institute reference in number 1 also gave data for the same 10 midsize luxury models for a 5-mph crash test that involved backing up into a flat barrier. The following data are listed for the cars in the same order as in Exercise 1.
01039 711 739 557 4181191 1042 322 390
a. Would the difference between the mean and the median be larger or smaller for this data set than it was for number 1? Why?
b. Compute the mean and the median for this data set. Write a sentence or two to interpret these two values.
c. Suppose that the first observation had been 500 rather than 0. How would the values of the mean and the median change?
d. Using the data given, calculate a trimmed mean by eliminating the smallest and the largest observations. What is the corresponding trimming percentage?
3. The October 1, 1994, issue of the San Luis Obispo Telegram reported the following monthly salaries for supervisors from six different counties: $5354 (Kern), $5166 (Monterey), $4443 (Santa Cruz), $4129 (Santa Barbara), $2500 (Placer), and $2220 (Merced). San Luis Obispo county supervisors are supposed to be paid the average of the two counties among these six in the middle of the salary range. Which measure of center determines this salary and what is its value? What is the other measure of center featured in this section not as favorable to these supervisors (although it might appeal to taxpayers)?
4. A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (in seconds) to complete the escape (“Oxygen Consumption and Ventilation During Escape from an Offshore Platform,” Ergonomics [1997]: 281-292):
a. Construct a stem-and-leaf display of the data. How does it suggest that the sample mean and median will compare? Explain.
b. Calculate the values of the sample mean and median.
c. By how much could the largest time be increased without affecting the value of the sample median?
d. By how much could the largest time be decreased without affecting the sample median?
5. The San Luis Obispo Telegram-Tribune (November 29, 1995) reported the values of the mean and median salary for major league baseball players for 1995. The values reported were $1,110,766 and $275,000.
a. Which of the two values do you think is the mean and which is the median? Explain.
b. The reported mean was computed using the salaries of all major league players in 1995. For the 1995 salaries, is the reported mean the population mean or the sample mean ? Explain.
6. Consider the following statement: “More than 65% of the residents of Los Angeles earn less than the average wage for that city.” Could this statement be correct? If so, how? If not, why not?
7. A sample consisting of four pieces of luggage was selected from among those checked at an airline counter, yielding the following data where x = weight (in pounds).
Suppose that one more piece is selected; denote its weight by . Find the value of such that .
8. An instructor has graded 19 exam papers submitted by students in a certain class of 20 students, and the average so far is 70. (The maximum possible score is 100). How high would the score on the last paper have to be to raise the class average by 2 points?
9. Out of a class of 36 students, 30 took their test on time and had an average of 88. The other six took it on the make-up test day and had an average of 92. What is the class average?
10. Sarah drove to her Aunt’s house for a visit. Since the was hardly any traffic, Sarah was able to drive the first 5 hours at a rate of 60 mph. But, as it neared 5 o’clock the traffic picked up and she was only able to drive 40 mph for the next 2 hours. What was her average speed?