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Lesson 1.7 %u2022 Measuring Variability 77 Lesson 1.7 W H AT D I D Y O U L E A R N ? LEARNING TARGET EXAMPLE EXERCISES Find the range of a distribution of quantitative data. p. 70 9%u201312 Calculate and interpret the standard deviation of a distribution of quantitative data. p. 71 13%u201316 Find and interpret the interquartile range of a distribution of quantitative data. p. 74 17%u201320 Building Concepts and Skills 1. The simplest measure of variability is the . 2. True/False: In the graph on page 70 , the range of the width of film strips made by Machine A is from 69.8 to 70.2 millimeters. 3. What is the formula for calculating the standard deviation of a sample of quantitative data? 4. True/False: The standard deviation should be interpreted as the typical distance of the values in a distribution from the mean. 5. Explain why the standard deviation of a distribution of quantitative data can never be negative. 6. How do you find the first quartile of a quantitative data set? 7. True/False: Range and standard deviation are nonresistant measures of variability, but interquartile range is a resistant measure. 8. For a skewed distribution or a distribution with outliers, use the to describe center and the to describe variability. Mastering Concepts and Skills 9. Midsize mileage Here are the EPA estimates of city gas mileage in miles per gallon (mpg) for a random sample of 21 midsize car models manufactured in the same year, along with a dotplot of the data. 91 Find the range of the distribution. 20 18 17 18 18 21 21 21 22 28 19 20 21 22 28 21 19 24 54 24 18 City gas mileage (mpg)15 20 25 30 35 40 45 50 5510. Soccer range How good was the 2019 U.S. women%u2019s soccer team? With players like Carli Lloyd, Alex Morgan, and Tobin Heath, the team put on an impressive showing en route to winning the 2019 Women%u2019s World Cup. Here are data on the number of goals scored by the team in games played in the 2019 season, along with a dotplot. 92 Find the range of the distribution. 1 1 2 2 1 5 6 3 5 3 13 3 2 2 2 2 2 3 4 3 2 1 3 6 Number of goals scored1 2 3 4 5 6 7 8 9 10 11 12 1311. Heart rates vary Here are the resting heart rates (in beats per minute) of 26 ninth-grade biology students. Find the range of the distribution. 61 48 77 81 78 75 70 77 70 76 86 55 65 60 63 79 62 71 72 74 74 64 66 71 66 68 12. Temperature range Here are the high temperature readings in degrees Fahrenheit for Phoenix, Arizona, for each day in July of a recent year. Find the range of the distribution. 111 84 115 108 106 109 111 113 104 103 97 99 104 110 109 100 105 107 102 101 107 93 101 105 99 102 104 108 106 106 109 13. Well rested? A random sample of 6 students in a first-period statistics class was asked how much sleep (to the nearest hour) they got last night. Their responses were 6, 7, 7, 8, 10, and 10 hours. Calculate the standard deviation. Interpret this value. 14. The rate of metabolism A person%u2019s metabolic rate is the rate at which their body consumes energy. Metabolic rate is important in studies of weight pg 70pg 71 Exercises %u00a9 Bedford, Freeman & Worth Publishers. For review purposes only. Do not distribute.