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MA 116 - Chapter 3 Review Name___________________________________ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place than that used for the observations. 1) 10, 17, 12, 10, 18 Find the median for the given sample data. 2) 11, 18, 19, 21, 30, 30, 49 Find the median for the data. Find the mode(s) for the given sample data. 3) -20, -26, -46, -26, -49, -26, -49 Provide an appropriate response. 4) The median of a data set is always/sometimes/never (select one) one of the data points in a set of data. Explain your answer with brief examples. 5) Suppose that a data set has a reverse J-shaped distribution. Which do you think will be larger, the mean or the median? Explain your thinking. Solve the problem. 6) Let x1 = 4, x2 = 18, x3 = 11, x4 = 1, and x5 = 15. Compute ·x . 7) The amount of money, in dollars, that an employee of a bank spent on lunch on six randomly selected days yielded the following data set. 8, 5, 5, 11, 4, 11 2 Compute ·x . 8) The amount of money, in dollars, that an employee of a bank spent on lunch on six randomly selected days yielded the following data set. 9, 14, 15, 5, 4, 13 Compute · (x - x) . 9) The amount of money, in dollars, that an employee of a bank spent on lunch on six randomly selected days yielded the following data set. 6, 12, 13, 9, 16, 13 2 Compute (x - x) · Find the range for the given data. 10) Jeanne is currently taking college economics. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores. 8 18 3 15 10 Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations. 11) 2, 6, 15, 9, 11, 22, 1, 4, 8, 19 1 Provide an appropriate response. 12) We want to compare two different groups of students, students taking Composition 1 in a traditional lecture format and students taking Composition 1 in a distance learning format. We know that the mean score on the research paper is 85 for both groups. What additional information would be provided by knowing the standard deviation? 13) A company advertises an average of 42,000 miles for one of its new tires. In the manufacturing process there is some variation around that average. Would the company want a process that provides a large or a small variance? Justify your answer. Determine the quartile or interquartile range as specified. 14) The test scores of 15 students are listed below. Find the first quartile, Q . 1 41 62 85 48 65 87 51 71 90 55 74 94 59 79 95 15) The test scores of 19 students are listed below. Find the interquartile range. 91 62 82 42 45 97 83 92 86 57 50 94 71 90 88 66 61 78 73 Obtain the five-number summary for the given data. 16) The test scores of 15 students are listed below. 41 63 85 47 64 87 51 69 90 55 75 94 56 79 95 Construct a boxplot or a modified boxplot as specified. 17) The weights (in pounds) of 30 newborn babies are listed below. Construct a boxplot for the data set. 5.5 5.7 5.8 5.9 6.1 6.1 6.3 6.4 6.5 6.6 6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2 7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7 Identify potential outliers, if any, for the given data. 18) The test scores of 15 students are listed below. 39 69 80 40 71 82 57 73 87 65 75 90 67 76 99 Solve the problem. 19) A variable x has a mean, m, of 25 and a standard deviation, s, of 7. Determine the standardized version of x. 2 Provide an appropriate response. 20) A group of medical researchers is interested in knowing the mean cholesterol level for all men in the U.S. aged between 70 and 80. They pick a sample of 5,000 men and measure their cholesterol levels. They then calculate the mean and standard deviation of these cholesterol levels. Do the mean and standard deviation obtained in this way represent parameters or statistics? Why? What symbols could you use to denote the mean and standard deviation of the 5,000 cholesterol levels? 3 Answer Key Testname: CHAPTER3.TST 1) Answer: 13.4 2) Answer: 21 3) Answer: -26 4) Answer: Answers will vary. Possible answer: The median is sometimes one of the data points. If the number of data points is odd, the median will be one of the data points (the middle data point). If the number of data points is even, the median is the average of the two middle data points which will be equal to one of the data points only if the two middle data points are identical. 5) Answer: The mean will be larger. Explanations will vary. Possible answer: A reverse J-shaped distribution is a special case of a right-skewed distribution since it contains a few extreme values lying far to the right of the bulk of the data. The mean is pulled in the direction of the extreme values, i.e. to the right. 6) Answer: 49 7) Answer: 1936 8) Answer: 0 9) Answer: 61.50 10) Answer: 15 11) Answer: 7.1 12) Answer: Answers will vary. Possible answer: The standard deviation will give an indication of how widely the scores vary. More precisely, it gives an indication of how much the scores deviate, on average, from the mean score of 85. 13) Answer: Answers will vary. Possible answer: A small standard deviation would be preferable as this would indicate that the lifetimes of the tires do not vary too widely. 14) Answer: 55 15) Answer: 29 16) Answer: 41, 55, 69, 87, 95 17) Answer: 18) Answer: 39 19) Answer: z = x - 25 7 20) Answer: The mean and standard deviation represent statistics since they are descriptive measures for a sample. They are denoted by x and s, respectively. 1