Measure that ball: Each of 16 students measured the circumference of a tennis ball by two different methods:

A: Estimate the circumference by eye.

B: Measure the circumference by rolling the ball along a ruler.

The results (in centimeters) are given below, in increasing order for each method:

a. Compute the sample standard deviation of the measurements for each method.

b. For which method is the sample standard deviation larger? Why should one expect this method to have the larger standard deviation?

c. 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.

Transcribed Image Text:

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 B: 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