Chapter 1, Problem 24SE

Aqua running has been suggested as a method of cardiovascular conditioning for injured athletes and others who desire a low-impact aerobics program. In a study to investigate the relationship between exercise cadence and heart rate,¹ the heart rates of 20 healthy volunteers were measured at a cadence of 48 cycles per minute (a cycle consisted of two steps). The data are as follows:

1. a Use the range of the measurements to obtain an estimate of the standard deviation.
2. b Construct a frequency histogram for the data. Use the histogram to retain a visual approximation to $\bar{y}$ and s.
3. c Calculate $\bar{y}$ and s. Compare these results with the calculation checks provided by parts (a) and (b).
4. d Construct the intervals $\bar{y}\pm ks,$, k = 1, 2, and 3, and count the number of measurements falling in each interval. Compare the fractions falling in the intervals with the fractions that you would expect according to the empirical rule.