Spring 2010 Practice Quiz 5 with Solutions

# During the early part of the 1994 baseball season

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18. During the early part of the 1994 baseball season, many sports fans and baseball players noticed that the number of home runs being hit seemed to be unusually large. Below is a stemplot of the team-by-team numbers of home runs hit through Friday, June 3, 1994, in both the American and National leagues. Stem Leaf 2 3 4 5 6 7 9 1 5 0 2 3 6 7 8 8 9 1 3 4 5 5 5 7 8 8 3 3 4 7 8 8 5 7 The five-number summary for the data is given by A. 29, 46.5, 55, 63, 77 B. 29, 46, 54.5, 63, 77 C. 29, 46.5, 54.5, 63.5, 77 D. NONE OF THESE THREE D B D

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8 The correct answer: 29, 46.5, 54.5, 63, 77 19. A sample was taken of the salaries of 20 employees of a large company. The following is a boxplot of the salaries (in thousands of dollars) for this year. Use this data to answer questions 19 21. 80 70 60 50 40 30 20 10 Which of the following statements follow from the boxplot: (i) The minimum salary is \$20,000 (ii) The maximum salary is \$60,000 (iii) The first quartile is \$20,000 (iv) The mean salary is \$50,000 (v) the third quartile is \$60,000? 20. Based on this boxplot, the five-number summary is Correct answer: 10, 20, 50, 60, 80. 21. Based on this boxplot, we can say that the proportion of employees in the sample with income over \$20,000 is Since 20 is the first quartile, 25% of the data falls to the left of 20. So there are 75% with income over\$20,000. The histogram below summarizes the final exam scores in Professor Bogdowne’s statistics class. Use it to answer questions 22 and 23 . Exam Scores 0 1 2 3 4 5 6 7 (7 0, 7 5 ] (75,80] (8 0 ,8 5 ] ( 85, 9 0] (9 0 ,95] ( 9 5 ,1 0 0] Scores Frequency 22. Which, if any, of the following statements are true? (i) The median score is 80 (ii) The mean score is at most equal to the median score (iii) The mean score cannot be below 80 (iv) The scores distribution is skewed to the left A. (i), (ii), and (iv) B. Only (ii) C. (ii) and (iv) D. NONE OF THESE THREE B D D D D
9 Since the distribution is skewed to the right we know that the mean should be to the right of the median. We know that the median has to be in the interval (75, 80] or in the interval (80,85] depending on the exact values of the 10 th observation (<= 80) and the 11 th observation (>80). Since we don’t know the location of the median relative to 80 we don’t know the position of the mean relative to 80. 23. What percent of the students scored below 80? A. At least 50% B. 50% C. At most 50% D. NONE OF THESE THREE We know that the number of students scoring below OR EQUAL to 80 is 10. So the number of students scoring below 80 should be 10 or less. 24. Below is a list of gas mileage ratings for selected passenger cars in miles per gallon: 53, 43, 89, 41, 85, 86, 91, 92, 95, 94, 86, 102, 114, 30, 123. Make a boxplot to represent this data. Data in increasing order: 30, 41, 43, 53, 85, 86, 86, 89, 91, 92, 94, 95, 102, 114, 123. There are 15 observations. The 8 th is the median = 89. The 4 th is Q1 = 53. The 12 th is Q3 = 95. Min = 30, Max = 123. 140 120 100 80 60 40 20 25. Create a set of five positive numbers that have median 6 and mean 10.

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