12.4 Measures of Dispersion 803 In Exercises 13–18, determine the standard deviation of the set of data. When appropriate, round the standard deviation to the nearest hundredth. 13. 7, 5, 2, 8, 13 ≈ 16.5 4.06 14. 12, 12, 16, 18, 10, 10 ≈ 10.8 3.29 15. 150, 151, 152, 153, 154, 155, 156 ≈ 4.67 2.16 16. 12, 16, 17, 21, 9, 18, 20, 21, 15, 11 ≈ 18 4.24 17. 4, 8, 9, 11, 13, 15 ≈ 15.2 3.90 18. 9, 9, 9, 9, 9, 9, 9 0 Problem Solving In Exercises 19–24, where appropriate, round standard deviations to the nearest hundredth. 19. Earbuds Determine the range and standard deviation of the following prices of selected earbuds: $299, $50, $300, $199, $173, $100, $399, $200. ≈ $349, 12,976 $113.91 20. Sugar in Cereal Determine the range and standard deviation of the following number of grams of sugar in selected cereals: 13, 6, 15, 2, 14, 6, 20, 0, 14. ≈ 20, 45.25 6.73 21. Camping Tents Determine the range and standard deviation of the following prices of selected camping tents: $109, $60, $80, $60, $210, $250, $60, $100, $115. ≈ $190, 4725.25 $68.74 22. Prescription Prices The amount of money seven people spent on prescription medication in a year are as follows: $600, $100, $850, $350, $250, $140, $300. Determine the range and standard deviation of the amounts. ≈ $750, 71,466.67 $267.33 23. Count Your Money Six people were asked to determine the amount of money they were carrying, to the nearest dollar. The results were $32, $60, $14, $25, $5, $68 a) Determine the range and standard deviation of the amounts. ≈ $63, 631.6 $25.13 b) Add $10 to each of the six amounts. How do you expect the range and standard deviation of the new set of data to change? Answers will vary. c) Determine the range and standard deviation of the new set of data. Do the results agree with your answer to part (b)? If not, explain why. Answers remain the same, range: $63, standard deviation ≈ $25.13 24. a) Five Numbers Pick any five numbers. Compute the mean and the standard deviation of this set of data. Answers will vary. b) Add 20 to each of the numbers in your original set of data and compute the mean and the standard deviation of this new set of data. Answers will vary. c) Subtract 5 from each number in your original set of data and compute the mean and standard deviation of this new set of data. Answers will vary. d) What conclusions can you draw about changes in the mean and the standard deviation when the same number is added to or subtracted from each piece of data in a set of data? If each piece of data is increased, or decreased, by n, the mean is increased, or decreased, by n. The standard deviation remains the same. e) How will the mean and standard deviation of the numbers 8, 9, 10, 11, 12, 13, 14 differ from the mean and standard deviation of the numbers 648, 649, 650, 651, 652, 653, 654? Determine the mean and standard deviation of both sets of numbers. Mean of first set is 11; mean of second set is 651. The standard deviation of both sets is ≈ 2.16. 25. a) Multiplying Each Number Pick any five numbers. Compute the mean and standard deviation of this set of data. Answers will vary. b) Multiply each number in your set of data by 3 and compute the mean and the standard deviation of this new set of data. Answers will vary. c) Multiply each number in your original set of data by 9 and compute the mean and the standard deviation of this new set of data. Answers will vary. d) What conclusions can you draw about changes in the mean and the standard deviation when each value in a set of data is multiplied by the same number? * e) The mean and standard deviation of the set of data 1, 3, 4, 4, 5, 7 are 4 and 2, respectively. Use the conclusion drawn in part (d) to determine the mean and standard deviation of the set of data 20, 10 5, 15, 20, 20, 25, 35 26. a) Multiplying Each Number Pick any six numbers. Compute the mean and standard deviation of this set of data. Answers will vary. b) Multiply each number in your set of data by 4 and compute the mean and standard deviation of this new set of data. Answers will vary. c) Multiply each number in your original set of data by 8 and compute the mean and standard deviation of this new set of data. Answers will vary. d) What conclusions can you draw about changes in the mean and the standard deviation when each value in a set of data is multiplied by the same number? * e) The mean and standard deviation of the set of data 5, 7, 8, 8, 9, 11 are 8 and 2 respectively. Use the conclusion drawn in part d) to determine the mean and standard deviation of the set of data 20, 28, 32, 32, 36, 44. 32, 8 DS $ DS DS $ DS $ *See Instructor Answer Appendix Insta_photos/Shutterstock
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