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%.