Chapter 3 case study: Engines. One measure of the size of an automobile engine i

Question

Chapter 3 case study: 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 displace- ments were measured in cubic inches. Summary of Displacement Count Mean Median 148.5 StdDev Range 275 25th%tile 105 75th%tile 231 38 177.29 88.88 a) How many cars were measured? b) Why might the mean be so much larger than the median? with appropriate statistics. engine he bought in his new car. Is that engine unusu- c) Describe the center and spread of this distribution d) Your neighbor is bragging about the 227-cubic-inch e) Are there any engines in this data set that you would f) s it reasonable to expect that about 68% of car engines ally large? Explain. consider to be outliers? Explain. 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. version affect each of the sum- mary statistics?

Explanation / Answer

(a)

The number of cars measured were 38

(b)

This is because the distribution is not symmetric about the mean, and the distribution is right skewed, which is why the mean is larger than the median.

(c)

In this case since the sample is not so large and might contain outliers, so median is a better measure of the central tendency as compared to mean.

So for this distribution:

Center = Median = 148.5

Spread = Standard deviation = 88.88

(d)

No, the value 227 lies within the 75th percentile number, so the value is not exceptionally big. It would have been unusually large if it would have lied outside the 75th percentile mark.

Hope this helps !

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