HOMEWORK #2 ANSWERS
Chapter 4
1. (a) Average = 50. Deviations = -9, -2, 0, 0, 4, 7. The SD is
(b) 48, 50, 50 are within 0.5 SDs of average, i.e., in the range 47.5-52.5.
48, 50, 50, 54, 57 are within 1.5 SDs of average, i.e., in the range 42.5-57.5.
4. For income, the average will be bigger than the median--long right hand tail at
work (pp. 64-65). For education, the average will be smaller than the median; the
histogram has a long left hand tail (p. 39).
6. (a) (i) 60 (ii) 50 (iii) 40
(b) (i) median is bigger than the average--long left hand tail
(ii) median is about equal to the average--symmetry
(iii) median is less than the average--long right hand tail
(c) 15: most of the area is within 50 of the average, so 50 is too big; only a little
of the area is within 5 of the average, so 5 is too small.
(d) False. Histograms (i) and (iii) are almost mirror images, and have just about
the same SD.
9. (a) Yes: the average goes up by ($986,000 - $98,600)/1000 = $887.40.
(b) No. (And that is one advantage of the median--it is not thrown off by outliers.)
11. $8, because the SD is 8, and the SD is the r.m.s. deviation from average.
Chapter 5
1. (a) 79% of 25
» 20.(b) 18.
4. (a) 20%
(b) 12%
6. No. For example, the normal curve says that about 16% of the scores should be
more than 1 SD above average, and none are.
8. (a) True. See pp.92ff.
(b) False: all the deviations from average stay the same.
(c) True.
(d) True: all the deviations from average are doubled.
(e) True.
(f) False: all the deviations from average have their signs changed, but that goes
away in the squaring. The SD has to be positive (or, exceptionally, zero).
10. The histogram has a long right hand tail; the median is well below average. Therefore, a lot less than 50% are earning about $35,000. Choose 40%.