Ch - Wake Forest University



Ch. 4 Review, p. 74: #1 – 10 all, but omit 7a

1. a) average = 50, SD = [pic] = 5

b) The numbers on the list within 0.5 SD’s = numbers in the interval 50 +/- 2.5: 48, 50, 50

The numbers on the list within 1.5 SD’s = numbers in 50 +/- 7.5: 48, 50, 50, 54, 57

2. a) List (ii) has the smaller SD because more entries are clustered near the average, making the list have less spread.

b) List (i) has the smaller SD because list (ii) has 2 entries that are way out.

3. a) The average is around 5 since some numbers are near 10, some near 1.

b) The SD is around 3 since about 95 % of the entries (in general) should be within +/- 2 SD’s, we know that 1 is not big enough, but 6 is too big.

4. The histogram for income for persons age 25 and over in the U.S. would have a long right hand tail, with Bill Gates and others stretching the histogram far and thin to the right. Since the average is the balance point, it would need to move to the right to “hold up” the tail. That means that the average would be larger than the median. For years of schooling, even though the histogram would have somewhat of a right-hand tail, with older people going back to school, the left-hand would have a tail as well since a lot of older people didn’t get to complete high school because of the depression, wars, etc. Right now, the average would probably be less than the median. However, as time goes on, and those who lived through the depression die, the median and the average will probably get closer and closer together. Within your lifetime, the average may overtake the median.

5. Since the average systolic blood pressure was 124 mm with an SD of 14 mm, we would expect about 68 % of the men to be in the range 110 mm to 138 mm; about 95 % of the men to be in the range 96 mm to 152 mm. This means that 80 mm is unusually low; 115 mm is about average; 135 mm is about average; 210 is unusually high.

6. a) The average of (i) is 60; of (ii) is 50; of (iii) is 40.

b) In (i) the median is bigger than the average, since the average would have to move left toward the tail. In (ii), the median would more or less equal the average. In (iii), the median would be less than the average.

c) The SD of histogram (iii) is around 15; +/- 5 doesn’t hold enough area, +/- 50 is too much.

d) False. Histogram (i) and (iii) are almost mirror images, so they would have similar SD’s.

7. a) omit

b) The interval 57 kg to 75 kg could be rewritten 66 kg +/- 9 kg, which is the average +/- 1 SD. That means that we would expect about 68 % to fall into that interval.

c) If the men’s and women’s weights were taken together, then the spread becomes much larger even though the groups would overlap, so the SD would be bigger than 9 kg.

8. a) Since the average height of the boys at age 11 was 146 cm, and the average height of all children (boys and girls) was 147 cm, the girls must be taller on average than the boys.

b) The best guess for the average height of 10 year old boys would be the average between 9 year olds and 11 year olds: 141 cm.

9. a) Since 98,600 was changed to 986,000 about 900,000 “extra” was added to the total before dividing by 1000 to get the average. This would affect the average by 900,000 ÷ 1000 = 900. The exact amount change would be $887.40.

b) This would not affect the middle score; it doesn’t care how far out the other scores are.

10. a) The best guess is the average: 163.

b) You have about a 1 in 3 chance to lose more than $8, since ⅔ should be within +/- 8 the SD.

11. a) Omit

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