Engines, again Horsepower is another measure commonly used

Chapter 5, Problem 7RE

(choose chapter or problem)

Problem 7RE

Engines, again Horsepower is another measure commonly used to describe auto engines. Here are the summary statistics and histogram displaying horsepowers of the same group of 38 cars discussed in Exercise.

Summary of Horsepower
Count	38
Mean	101.7
Median	100
StdDev	26.4
Range	90
25th %tile	78
75th %tile	125

a) Describe the shape, center, and spread of this distribution.

b) What is the interquartile range?

c) Are any of these engines outliers in terms of horsepower? Explain.

d) Do you think the 68–95–99.7 Rule applies to the horsepower of auto engines? Explain.

e) From the histogram, make a rough estimate of the percentage of these engines whose horsepower is within one standard deviation of the mean.

f) A fuel additive boasts in its advertising that it can “add 10 horsepower to any car.” Assuming that is true, what would happen to each of these summary statistics if this additive were used in all the cars?

Exercise

Engines One measure of the size of an automobile engine is its “displacement,” the total volume (in liters or cubic inches) of its cylinders. Summary statistics for several models of new cars are shown. These displacements were measured in cubic inches.

Summary of Displacement
Count	38
Mean	177.29
Median	148.5
StdDev	88.88
Range	275
25th %tile	105
75th %tile	231

a) How many cars were measured?

b) Why might the mean be so much larger than the median?

c) Describe the center and spread of this distribution with appropriate statistics.

d) Your neighbor is bragging about the 227-cubic-inch engine he bought in his new car. Is that engine unusually large? Explain.

e) Are there any engines in this data set that you would consider to be outliers? Explain.

f) Is it reasonable to expect that about 68% of car engines measure between 88 and 266 cubic inches? (That’s 177.289 ± 88.8767.) Explain.

g) We can convert all the data from cubic inches to cubic centimeters (cc) by multiplying by 16.4. For example, a 200-cubic-inch engine has a displacement of 3280 cc. How would such a conversion affect each of the summary statistics?