Practice Problems for Section 6.1 with Solutions

Practice Problems for Section 6.1 The mean of a list of numbers is the product of the numbers divided by the number of entries in the list. A) True (B) False The median of a list of numbers arranged from smallest to largest is the middle number.   If a number in a data set occurs more frequently than any other number, it is called the ____ of the data. A) mean B) median (C) mode D) average   A(n) ____ is a data point that is significantly different from most of the data. A) foreigner (B) outlier C) quartile D) anomaly The ____ quartile is the median of the upper half of the numbers in a list. A) first B) second (C) third D) fourth Which of the following is not included in the five-number summary? A) Median B) Maximum C) Third quartile (D) Mode   7. The standard deviation is a measure of how much the data are spread out from the mean. * A) True * B) False 8. A(n) histogram_ is a bar graph that shows the frequencies with which certain data occur. * A) histogram * B) boxplot * C) scatterplot * D) line graph 9. Michael's five test scores in his physics class were 75, 67, 88, 91, and 84. What was his mean test score?   (75 + 67 + 88 + 91 + 84) / 5 = 81 10. Michael's five test scores in his physics class were 75, 67, 88, 91, and 84. What was his median test score? 67, 75, 84, 88, 91 = 84 11. XYZ Corporation recorded the number of employee absences each week over a period of 10 weeks. The result is the data list 5, 3, 4, 1, 4, 7, 2, 6, 3, 5. Find the mean number of absences each week.   (5 + 3 + 4 + 1 + 4 + 7 + 2 + 6 + 3 + 5) / 10 = 4 12. XYZ Corporation recorded the number of employee absences each week over a period of 10 weeks. The result is the data list 5, 3, 4, 1, 4, 7, 2, 6, 3, 5. Find the standard deviation of the number of absences each week.   1.83 (Please see class notes) 13. Suppose that every student in your class scored 75% on their first test. Find the standard deviation of the exam scores.   0 Since all students scored 75%, the standard deviation is zero. 14. A class has an equal number of boys and girls. The boys all got 77% on a test and the girls all got 83%. What is the standard deviation of the test scores for the class?   3.00 Since all boys got 77% on the test and all girls got 83% on the test, the mean is 80% and the standard deviation is 3%. 15. An auto dealer's sales numbers are shown in the table below. Find the mean price for the cars sold in June. Price June July August $25,000 21 23 24 $20,000 35 32 37 $15,000 47 51 44 Calculation: (21 * $25,000) + (35 * $20,000) + (47 * $15,000) = $1,873,500 $1,873,500 / 103 (total cars sold in June) = $18,736.86 16. An auto dealer's sales numbers are shown in the table below. Find the median price for the cars sold in July. Price June July August $25,000 21 23 24 $20,000 35 32 37 $15,000 47 51 44 Calculation: Arranging the prices based on the number of cars sold in July: $15,000, $15,000, ..., $15,000, $20,000, $20,000, ..., $20,000, $25,000, $25,000, ... The median price is $20,000. 17. An auto dealer's sales numbers are shown in the table below. Find the mode price for the cars sold in August. Price June July August $25,000 21 23 24 $20,000 35 32 37 $15,000 47 51 44 Answer: $15,000 Explanation: $15,000 appears the most in August. 18. Ted's six test scores in a biology class were 66, 46, 87, 74, 80, and 56. What was his average test score if his lowest test grade were dropped?   Calculation: (66 + 87 + 74 + 80 + 56) / 5 = 73 19. A class has 11 boys and 19 girls. The class as a whole has a grade-point average (GPA) of 2.84, and the boys have a GPA of 2.51. What is the GPA of the girls?   Calculation: Let GPA of girls = X 11 * 2.51 + 19 * X = 30 * 2.84 Solving for X, we get GPA of girls = 3.03