SECTION 2.4 Measures of Variation 95 20. Salary Offers You are applying for jobs at two companies. Company C offers starting salaries with m = $59,000 and s = $1500. Company D offers starting salaries with m = $59,000 and s = $1000. From which company are you more likely to get an offer of $62,000 or more? Explain your reasoning. Graphical Analysis In Exercises 21–24, you are asked to compare three data sets. (a) Without calculating, determine which data set has the greatest sample standard deviation and which has the least sample standard deviation. Explain your reasoning. (b) How are the data sets the same? How do they differ? (c) Estimate the sample standard deviations. Then determine how close each of your estimates is by finding the sample standard deviations. 21. (i) (ii) (iii) 10 11 12 13 14 10 11 12 13 14 10 11 12 13 14 22. (i) (ii) (iii) Data entry Frequency 1 3 2 4 6 5 4 5 6 7 8 9 10 Data entry Frequency 1 3 2 4 6 5 4 5 6 7 8 9 10 Data entry Frequency 1 3 2 4 6 5 4 5 6 7 8 9 10 23. (i) 0 9 1 5 8 2 3 3 7 7 3 2 5 4 1 (ii) 0 9 1 5 2 333777 3 5 4 1 (iii) 0 1 5 2 33337777 3 5 4 Key: 10 5 = 15 Key: 10 5 = 15 Key: 10 5 = 15 24. (i) (ii) (iii) 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Constructing Data Sets In Exercises 25–28, construct a data set that has the given statistics. 25. N = 6 26. N = 8 m = 5 m = 6 s ≈ 2 s ≈ 3 27. n = 7 28. n = 6 x = 9 x = 7 s = 0 s = 2
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