Chapter 1.2, Problem 13E

Refer to Exercise 12.

1. a. If the measurements for one of the methods were converted to inches (1 inch = 2.54 cm), how would this affect the mean? The median? The quartiles? The standard deviation?
2. b. If the students remeasured the ball, using a ruler marked in inches, would the effects on the mean, median, quartiles, and standard deviation be the same as in part (a)? Explain.

12.    Each of 16 students measured the circumference of a tennis ball by four different methods, which were:

Method A: Estimate the circumference by eye.

Method B: Measure the diameter with a ruler, and then compute the circumference.

Method C: Measure the circumference with a ruler and string.

Method D: Measure the circumference by rolling the ball along a ruler.

The results (in cm) are as follows, in increasing order for each method:

Method A: 18.0, 18.0, 18.0, 20.0, 22.0, 22.0, 22.5, 23.0, 24.0, 24.0, 25.0, 25.0, 25.0, 25.0, 26.0, 26.4.

Method B: 18.8, 18.9, 18.9, 19.6, 20.1, 20.4, 20.4, 20.4, 20.4, 20.5, 21.2, 22.0, 22.0, 22.0, 22.0, 23.6.

Method C: 20.2, 20.5, 20.5, 20.7, 20.8, 20.9, 21.0, 21.0, 21.0, 21.0, 21.0, 21.5, 21.5, 21.5, 21.5, 21.6.

Method D: 20.0, 20.0, 20.0, 20.0, 20.2, 20.5, 20.5, 20.7, 20.7, 20.7, 21.0, 21.1, 21.5, 21.6, 22.1, 22.3.

1. a. Compute the mean measurement for each method.
2. b. Compute the median measurement for each method.
3. c. Compute the 20% trimmed mean measurement for each method.
4. d. Compute the first and third quartiles for each method.
5. e. Compute the standard deviation of the measurements for each method.
6. f. For which method is the standard deviation the largest? Why should one expect this method to have the largest standard deviation?
7. g. Other things being equal, is it better for a measurement method to have a smaller standard deviation or a larger standard deviation? Or doesn’t it matter? Explain.