14 MCQs in Statistics ...

3. Find the variance S^2of a sample for which the following information is given: n = 5, ∑▒X= 15, ∑▒X^2 = 47. (a) S^2 = 9 (b) S^2= 3 (c) S^2= .71 (d) S^2= .50 (e) cannot be determined from the data 

Problems 4 through 6 pertain to the following sample data: 10, −5, 13, 22, 4, 8, 12, −1, 0 

4. The mean of this data set is about: (a) 8.3 (b) 8.4 (c) 9.0 (d) 7.0 (e) 8.0 

5. The median of this data set is about: (a) 4.0 (b) 3.94 (c) 8.0 (d) 7.04 (e) 9.13 

6. The sample standard deviation of this data set is about: (a) 8.4 (b) 7.9 (c) 5.7 (d) 70.3 (e) 62.4 

7. Weights of three year old girls have a mound-shaped and symmetric distribution, with mean 14 kg and standard deviation 1 kg. The proportion of all three year old girls who weigh at least 16 kg is about: 7.5% (b) 2.5% (c) 5.0% (d) 95.0% (e) 97.5% 

8. Scores of 50 students on a college exam are: 75 83 92 68 74 66 94 80 78 86 67 94 77 78 85 65 73 77 81 69 82 74 80 63 78 86 97 74 72 64 73 74 88 90 76 82 69 65 79 88 63 83 77 75 84 68 76 85 70 93 The percentile rank of the score 78 is about: (a) 58 (b) 83 (c) 26 (d) 78 (e) 52 

9. A driver on his way to work passes through a certain intersection twenty times per month. The traffic light is green for his direction of travel 65% of the time. The average number of times per month that the light is green for his direction of travel when he reaches the intersection is about: (a) 12 (b) 15 (c) 13 (d) 7 (e) impossible to tell from the information given 

10. The standard deviation of a data set measures the________________ of the data set. (a) most frequent value (b) variability (c) size (d) range (e) average 

11. A real estate agent wishes to estimate the mean number of days on the market of all houses sold in the last two years in Mecklenburg County. To do so, he examines the sales data of fifty randomly selected houses sold in that period. The population of interest to the agent is: (a) All houses sold in Mecklenburg County in the last two years. (b) All houses sold that were not in the sample. (c) The fifty houses in the sample. (d) All houses sold except the fifty in the sample. (e) None of the above. 

12. The distribution of the ages in years of missing children aged one to nine is roughly bell–shaped, with a mean of about 5.5 and a standard deviation of about 2. The proportion of such children who are three and a half or younger is about (a) .84 (b) .68 (c) .32 (d) .95 (e) .16 

13. If the number 10 is added to each value of a data set, then: (a) The mean goes up by 10 and the standard deviation stays the same. (b) The mean goes up by 10 and the standard deviation goes up by √10 (c) The mean goes up by 10 and the standard deviation goes down by √10 (d) The mean and the standard deviation both stay the same. (e) It is impossible to tell what happens to both the mean and the standard deviation. 

14. Weights of one year old boys have a bell-shaped distribution with mean 27 pounds and standard deviation 3 pounds. The proportion of all one year old boys who weigh at least 30 pounds is about: (a) 84% (b) 95% (c) 68% (d) 5% (e) 16% 

15. A mother is told that her one year old son’s weight is the 75th percentile. This implies that: (a) Her son weighs 75% of the average weight of all one year old boys. (b) Her son weighs more than 75% of all one year old boys. (c) Her son weighs less than 75% of all one year old boys. (d) The z-score of her son’s weight is .75. (e) None of the above. 

16 A landfill manager estimates that the weight of the trash on arriving trucks has bell shaped distribution with mean 45 tons and standard deviation 7 tons. The proportion of trucks whose load exceeds 52 tons is about: (a) .16 (b) .025 (c) .84 (d) .34 (e) .68