Chapter 3: Q5 (page 127)
Sleep Outlier If the sleep time of 0 hours is included with the sample data given in Exercise 1, is it an outlier? Why or why not?
Yes, the zero-hour value is an outlier in the dataset.
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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
Firefighter Fatalities Listed below are the numbers of heroic firefighters who lost their lives in the United States each year while lighting forest fires. The numbers are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures of center?
20 18 23 30 20 12 24 9 25 15 8 11 15 34
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. Herewe find measures of variation.) Then answer the given questions.
What Happens in Vegas . . . Listed below are prices in dollars for one night at different hotels located on Las Vegas Boulevard (the “Strip”). How useful are the measures of variation for someone searching for a room?
212 77 121 104 153 264 195 244
In Exercises 9 –12, consider a value to be significantly low if its z score is less than or equal to -2 or consider the value to be significantly high if its z score is greater than or equal to 2.
MCAT In a recent year, scores on the Medical College Admission Test (MCAT) had a mean of 25.2 and a standard deviation of 6.4. Identify the MCAT scores that are significantly low or significantly high.
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
Quadratic Mean The quadratic mean (or root mean square, or R.M.S.) is used in physical applications, such as power distribution systems. The quadratic mean of a set of values is obtained by squaring each value, adding those squares, dividing the sum by the number of values n, and then taking the square root of that result, as indicated below:
Find the R.M.S. of these voltages measured from household current: 0, 60, 110, -110, -60, 0.
How does the result compare to the mean?
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