Concept explainers
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.
- a. Compute the mean measurement for each method.
- b. Compute the median measurement for each method.
- c. Compute the 20% trimmed mean measurement for each method.
- d. Compute the first and third
quartiles for each method. - e. Compute the standard deviation of the measurements for each method.
- f. For which method is the standard deviation the largest? Why should one expect this method to have the largest standard deviation?
- 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.
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