According to the 95% rule, the largest value in a sample from a distribution which is approximately symmetric and bell-shaped should be between 2 and 3 standard deviations above the mean, while the smallest value should be between 2 and 3 standard deviations below the mean. Thus the range should be roughly 4 to 6 times the standard deviation. As a rough rule of thumb, we can get a quick estimate of the standard deviation for a bell-shaped distribution by dividing the range by 5. Check how well this quick estimate works in the following situations.

(a) Pulse rates from the StudentSurvey dataset discussed in Example 2.17 on page 77. The five number summary of pulse rates is (35, 62, 70, 78, 130) and the standard deviation is s = 12.2 bpm. Find the rough estimate using all the data, and then excluding the two outliers at 120 and 130, which leaves the maximum at 96.

(b) Number of hours a week spent exercising from the StudentSurvey dataset discussed in Example 2.21 on page 81. The five number summary of this dataset is (0, 5, 8, 12, 40) and the standard deviation is s = 5.741 hours.

(c) Longevity of mammals from the Mammal- Longevity dataset discussed in Example 2.22 on page 82. The five number summary of the longevity values is (1, 8, 12, 16, 40) and the standard deviation is s = 7.24 years.