Engines One measure of the size of an automobile engine is

Chapter 5, Problem 31RE

(choose chapter or problem)

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.

\(\begin{array}{l}\text{ Summary of Displacement }\\ \begin{array}{l|c}\text{ Count }&38\\ \text{ Mean }&177.29\\ \text{ Median }&148.5\\ \text{ StdDev }&88.88\\ \text{ Range }&275\\ \text{ 25th %tile }&105\\ \text{ 75th %tile }&231\end{array}\end{array}\)

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 \pm 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?