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Self Assessment for Lesson 8 1. Click on “Begin Assessment” button. 2. Scroll down to begin quiz. 1 Self Assessment for Lesson 8 2 1. Compare the centers of Distribution A (Female Shoulder Girth) and Distribution B (Male Shoulder Girth) shown below. Distribution A Distribution B 60 30 40 20 20 10 0 0 80 86 92 98 104 110 116 122 Female Shoulder Girth (cm) 128 134 100 104 108 112 116 120 124 128 132 136 Male Shoulder Girth (cm) The center of Distribution A is greater than the center of Distribution B. The center of Distribution A is less than the center of Distribution B. The center of Distribution A is equal to the center of Distribution B. Self Assessment for Lesson 8 3 2. Compare the spreads of Distribution A (Female Shoulder Girth) and Distribution B (Male Shoulder Girth) shown below. Distribution A Distribution B 60 30 40 20 20 10 0 0 80 86 92 98 104 110 116 122 Female Shoulder Girth (cm) 128 134 100 104 108 112 116 120 124 128 132 136 Male Shoulder Girth (cm) The spread of Distribution A is greater than the spread of Distribution B. The spread of Distribution A is less than the spread of Distribution B. The spread of Distribution A is equal to the spread of Distribution B. Self Assessment for Lesson 8 4 3. What is the approximate range of the Male Wrist Girth dataset shown below? 14 15 16 17 18 Male Wrist Girth (cm) 19 20 Self Assessment for Lesson 8 5 4. What is the approximate interquartile range of the Male Wrist Girth dataset? 14 15 16 17 18 Male Wrist Girth (cm) 19 20 Self Assessment for Lesson 8 6 5. If a dataset contains outliers, which measure of spread is resistant? Range Interquartile Range Standard Deviation Variance 6. Which of the following statements is TRUE? Standard deviation has no unit of measurement. Standard deviation is either positive or negative. Standard deviation is inflated by outliers. Standard deviation is used even when the mean is not an appropriate measure of center. Self Assessment for Lesson 8 7 7. For the following distribution of major league baseball players’ salaries in 1992, which measures of center and spread are more appropriate? 1992 Major League Baseball Players’ Salaries 100 80 60 40 20 0 0 640 1280 1920 2560 3200 3840 4480 5120 Salary in Thousands of Dollars mean and standard deviation median and interquartile range 5760 6400 Self Assessment for Lesson 8 8. Which dataset has the largest value for s? A * * * * * * * * * 10 20 * 50 B * ***** * **** 80 A B C C * * 60 **** 90 8 Self Assessment for Lesson 8 9 Click on the “Grade Quiz” button to see how you did. Questions correct: Percentage correct: Click on the “Correct” button to highlight your correct answers in green and wrong answers in red. For question solutions either: • shift-click on the “Ans” button that appears next to the free-response box or • shift-click on the correct answer for the multiple choice questions. Solutions to Quizzes 10 Solutions to Quizzes Solution to Quiz: 1. The center of Distribution A is approximately 100. The center of Distribution B is approximately 116. The center of Distribution A is less than the center of Distribution B End Quiz Solutions to Quizzes 11 Solution to Quiz: 2. Because the shape of both distributions is nearly symmetric, we can use the range to compare their spreads. The minimum value in Distribution A is approximately 85 and the maximum value is approximately 130. The minimum value in Distribution B is approximately 100 and the maximum value is approximately 135. The approximate range of Distribution A (45) is greater than the approximate range of Distribution B (35). Visually, the spread of Distribution B looks larger; however, because the scales are different, we need to compute the ranges to compare the spreads. End Quiz Solutions to Quizzes 12 Solution to Quiz: 3. The range is defined as the maximum value minus the minimum value. As indicated by the boxplot, the maximum value is approximately 19.5 and the minimum value is approximately 14.5. The range approximately equals 5. End Quiz Solutions to Quizzes 13 Solution to Quiz: 4. The interquartile range is defined as Q3 minus Q1. As indicated by the boxplot, Q3 is approximately 18 and Q1 is approximately 16.5. The interquartile range approximately equals 1.5. End Quiz Solutions to Quizzes 14 Solution to Quiz: 5. The standard deviation, variance, and range are all sensitive to outliers. The interquartile range is resistant to outliers. End Quiz Solutions to Quizzes 15 Solution to Quiz: 6. Standard deviation has the same unit of measurement as the original observations, is positive or zero, and is inflated by outliers. The standard deviation measures the spread about the mean and should only be used when the mean is an appropriate measure of center. End Quiz Solutions to Quizzes 16 Solution to Quiz: 7. The mean and standard deviation are affected by skewness. End Quiz Solutions to Quizzes 17 Solution to Quiz: 8. Dataset C has the largest spread of data (standard deviation) about the mean. End Quiz