3-2 Measures of Variation 119 28. Weights Use the weights of the males listed in Data Set 2 “ANSUR I 1988,” which were measured in 1988 and use the weights of the males listed in Data Set 3 “ANSUR II 2012,” which were measured in 2012. Does it appear that amounts of variation have changed from 1988 to 2012? Estimating Standard Deviation with the Range Rule of Thumb. In Exercises 29–32, refer to the data in the indicated exercise. After finding the range of the data, use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the standard deviation computed using all of the data. 29. Exercise 25 “Body Temperatures” 30. Exercise 26 “Earthquakes” 31. Exercise 27 “Audiometry” 32. Exercise 28 “Weights” Identifying Significant Values with the Range Rule of Thumb. In Exercises 33–36, use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. 33. U.S. Presidents Based on Data Set 22 “Presidents” in Appendix B, at the time of their first inauguration, presidents have a mean age of 55.2 years and a standard deviation of 6.9 years. Is the minimum required 35-year age for a president significantly low? 34. Pulse Rates of Males Based on Data Set 1 “Body Data” in Appendix B, males have pulse rates with a mean of 69.6 beats per minute and a standard deviation of 11.3 beats per minute. Is a pulse rate of 50 beats per minute significantly low, significantly high, or neither? (All of these pulse rates are measured at rest.) Explain. 35. Foot Lengths Based on Data Set 9 “Foot and Height” in Appendix B, adult males have foot lengths with a mean of 27.32 cm and a standard deviation of 1.29 cm. Is the adult male foot length of 30 cm significantly low, significantly high, or neither? Explain. 36. Body Temperatures Based on Data Set 5 “Body Temperatures” in Appendix B, body temperatures of adults have a mean of 98.20°F and a standard deviation of 0.62°F. (The data from 12 AM on day 2 are used.) Is an adult body temperature of 100oF significantly low, significantly high, or neither? Finding Standard Deviation from a Frequency Distribution. In Exercises 37–40, refer to the frequency distribution in the given exercise and compute the standard deviation by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviations to these standard deviations obtained by using Formula 3-4 with the original list of data values: (Exercise 37) 18.5 minutes; (Exercise 38) 36.7 minutes; (Exercise 39) 6.9 years; (Exercise 40) 20.4 seconds. Standard deviation for frequency distribution s = Cn3Σ1f # x224 - 3Σ1f # x242 n1n - 12 37. Daily Commute Time in Los Angeles, CA (minutes) Frequency 0–14 6 15–29 18 30–44 14 45–59 5 60–74 5 75–89 1 90–104 1 38. “Avatar Flight of Passage” Wait Times 10 AM (minutes) Frequency 70–89 4 90–109 7 110–129 6 130–149 6 150–169 18 170–189 5 190–209 1 210–229 3
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