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Unformatted text preview: Homework 01134 Solutions Chapter 3 I. 56 and 72 inches. 2. a. Since the histogram is higher at 1 year than at 11 years1 there are more children atage 1.
b. More 31yearolds. c. More age 3544 because the area of the corresponding block is bigger than the one
corresponding to 3044. d. It is closest to 50%. 3. a. This is due to rounding when reporting percentages. 13. No. Percentages adjust for the diﬁ'erence between total numbers.
c. Owner occupiedunits. 4. (a) 25%, (b) 99%, (c) 140—150, (d) 135—140
(e) 2.1%fn1m x (130 — 125)mm = 10.5%, (1') 102—103 (g) 11?—118 mm (right in the middle), but there are other possible choices, such as 116117
mm or 118—119 mm. 6. (i) and (ii) only because heights are measured to the nearest eighth of an inch. 9. (a) True, (b) True (c) Students with a GPA below 2 probably round it up. Those with GPA slightly above 2
may round it down. [0 {a} 20 10 (d) In JSSU. [here was a strong preference for even digits (although 4 and 6 lose our to 5); again, this is probably due to rounding. In 19H), the preference was
much weaker. Chapter 4. 1. (3] Average = 50. Deviations = 9. —31 0. 01 4' 7' The SD '5 (—9)1+ (—2)? +02 +02 +42 +7: = 5.
—'—6—‘‘—"—'— (b) 48. 50, 50 are within 0.5 SDs of average, i.e., in the range 47.5—52.5.
43, 50. 50, 54. S? are within 1.5 SDs of average. i.e.. in the range 42.567.5. 3. a. The numbers are at most 9.9, so the average can not be 10. On the other hand, few numbers are close to 1 compared to the others, so the average is certainly not 1. It has to
be around 5. b. Around 3. The SD can not be around 1 because the smallest and largest numbers (0.6
and 9.9) would be about 5 SDs far away from the average (5). An SD of 6 is too big since
all the numbers would be less than 1 SD away from the average. 4. The histogram of income (on pp.6465) has a long right hand tail, so the average is bigger.
For education, histogram on page 39 has a long left hand tail, so the average is smaller. 5. Look at the standing of each blood pressure in terms of SD about the average. 80 mm is
below the average by more than 3 SDs, hence is unusually low. 115, and 135 mm are about
average, and 210 mm is unusually high (more than 6 SDs above average). 6.
a. (i) 61), (ii) 50, (iii) 40 b. (i) median is bigger than the average, (ii) median is about equal to the average, {iii}
median is less that the average c. The SD can not be 5, because the area within 3 SDs of the mean would be around
45% (it should have been at least 95%}. Similarly, the SD can not be 50, because all the
measurements would be within 1 SD around the mean. The SD has to be close to 15.
(1. False. The two histograms are almost mirror images. Their SDs are almost equal. ’3". a. For men: ave a: 145 ponds with an SD of about 20 pounds. For women, ave x 121
pounds with an SD of about 20 pounds.
I). 68% [within one SD) c. bigger than 9 kg. The spread of the weights for men and women taken together goes up. ...
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 Spring '08
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