Chapter 3: Q9 (page 127)
Estimating s A large sample of sleep times includes values ranging from a low of 4 hours to a high of 10 hours. Use the range rule of thumb to estimate the standard deviation.
The estimated standard deviation obtained by using the range rule of thumb is 1.5 hours.
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In Exercises 37–40, refer to the frequency distribution in the given exercise and find 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) 11.5 years; (Exercise 38) 8.9 years; (Exercise 39) 59.5; (Exercise 40) 65.4.
Standard deviation for frequency distribution
Age (yr) of Best Actress When Oscar Was Won | Frequency |
20-29 | 29 |
30-39 | 34 |
40-49 | 14 |
50-59 | 3 |
60-69 | 5 |
70-79 | 1 |
80-89 | 1 |
In Exercises 21–24, find the coefficient of variation for each of the two samples; then compare the variation. (The same data were used in Section 3-1.) 21.
Pulse Rates Listed below are pulse rates (beats per minute) from samples of adult males and females (from Data Set 1 “Body Data” in Appendix B). Does there appear to be a difference?
Male: 86 72 64 72 72 54 66 56 80 72 64 64 96 58 66
Female: 64 84 82 70 74 86 90 88 90 90 94 68 90 82 80
Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question
Most Expensive Colleges Listed below are the annual costs (dollars) of tuition and fees at the 10 most expensive colleges in the United States for a recent year (based on data from U.S. News & World Report). The colleges listed in order are Columbia, Vassar, Trinity, George Washington, Carnegie Mellon, Wesleyan, Tulane, Bucknell, Oberlin, and Union. What does this “top 10” list tell us about those costs for the population of all U.S. college tuitions?
49,138 47,890 47,510 47,343 46,962 46,944 46,930 46,902 46,870 46,785
In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here, we find measures of variation.) Then answer the given questions.
Foot Lengths Listed below are foot lengths in inches of randomly selected Army women measured in the 1988 Anthropometric Survey (ANSUR). Are the statistics representative of the current population of all Army women?
10.4 9.3 9.1 9.3 10.0 9.4 8.6 9.8 9.9 9.1 9.1
z Scores If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: -2.00, -1.00, 0, 1.00, 2.00? Why?
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