Chapter 3: Central Tendency - Solutions

Chapter 3: Central Tendency 1. The purpose of central tendency is to identify a single score that serves as the best representative for an entire distribution, usually a score from the center of the distribution. 2. No single method for computing a measure of central tendency works well in all situations. With three different methods, however, at least one usually works well 3. The mean is 27/10 = 2.7, the median is 2.5, and the mode is 2. 4. For this sample, the mean, median, and mode are all 7. 5. The mean is 40/12 = 3.33, the median is 3.50, and the mode is 4. 6. The mean is 152/20 = 7.6, the median is 7.5, and the mode is 7. 7. a. Median = 2.25 b. Median = 2 8. His median position is 2nd. 9. ΣX = 48. 10. ΣX = 250 11. The original sample has n = 8 and ΣX = 80. The new sample has n = 9 and ΣX = 81. The new mean is M = 9. 14. The original sample has n = 5 and ΣX = 60. The new sample has n = 4 and ΣX = 52. The new mean is M = 13. 15. The new mean is 48/6 = 8. Changing X = 14 to X = 2 subtracts 12 points from ΣX . 16. The new mean is 176/8 = 22. Changing X = 14 to X = 30 adds 16 points to ΣX . 17. The original sample has n = 7 and ΣX = 35. The new sample has n = 8 and ΣX = 48. The new score must be X = 13. 18. The original sample has n = 10 and ΣX = 90. The new sample has n = 9 and ΣX = 72. The score that was removed must be X = 18. 19. a. The new mean is M = 6. b. The new mean is (12 + 56)/10 = 6.8. c. The new mean is (28 + 24)/10 = 5.2. 20. a. The new mean is 90/10 = 9. b. The new mean is (24 + 96)/12 = 10 c. The new mean is (48 + 48)/12 = 8 21. The combined mean is (56 + 36)/10 = 9.2. 22. The combined mean is (1000 + 50)/25 = 42. 23. With a skewed distribution, the extreme scores in the tail can displace the mean out toward the tail. The result is that the mean is often not a very representative value. 12. The new mean is 147/21 = 7. 13. The new mean is 198/9 = 22. 24. The median is used instead of the mean when there is a skewed distribution (a few extreme scores), an open-ended distribution, undetermined scores, or an ordinal scale. 25. a. median (a few extreme scores would distort the mean) b. mode (nominal scale) c. mean 26. a. Mode = 2 b. Median = 2 c. You cannot find the total number of fast-food visits (ΣX) for this sample. 27. a. 5 │ │ 4 │ ┌───┐ │ │ │ 3 │ ┌───┬───┤ │ │ │ │ │ │ 2 │ ┌───┐ │ │ │ ├───┐ ┌───┐ f │ │ │ │ │ │ │ │ │ │ 1 │ ┌───┬───┤ ├───┤ │ │ │ ├───┤ │ │ │ │ │ │ │ │ │ │ │ │ │ └─┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴─ X −2 −1 0 +1 +2 +3 +4 +5 +6 +7 Pain level before treatment relative to after treatment b. The mean difference in pain level is M = 59/20 = 2.95. On average, pain was greater by an average of 2.95 points before treatment. c. Yes, the pain level was higher before treatment for nearly all the participants. 28. a. For weekdays M = 0.99 inches and for weekend days is M = 1.67 inches. b. There does appear to be more rain on weekend days than there is on weekdays.