AP Stats
Measures of Center
Name______________________________
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.
Model
Repair Cost
Model
Audi A6
0
lexus IS300
BMW 328i
0
Mercedes C320
Cadillac Catera
900
Saab 9-5
Jaguar X
1254
Volvo S60
Lexus ES300
234
Volvo S 80
*Included cost to replace airbags, which deployed.
Repair Cost
979
707
670
769
4194*
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.
0
1039
711
739
557
418
1191
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):
389
373
392
356
373
369
359
370
374
363
364
359
375
366
359
424
364
403
325
325
334
394
339
397
402
393
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?