2.4 EXERCISES SECTION 2.4 Measures of Variation 93 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. Explain how to find the range of a data set. What is an advantage of using the range as a measure of variation? What is a disadvantage? 2. Explain how to find the deviation of an entry in a data set. What is the sum of all the deviations in any data set? 3. Why is the standard deviation used more frequently than the variance? 4. Explain the relationship between variance and standard deviation. Can either of these measures be negative? Explain. 5. Describe the difference between the calculation of population standard deviation and that of sample standard deviation. 6. Given a data set, how do you know whether to calculate s or s? 7. Discuss the similarities and the differences between the Empirical Rule and Chebychev’s Theorem. 8. What must you know about a data set before you can use the Empirical Rule? Using and Interpreting Concepts Finding the Range of a Data Set In Exercises 9 and 10, find the range of the data set represented by the graph. 9. Frequency 3 6 9 12 45 50 55 60 65 70 75 80 85 90 95 Income (in thousands of dollars) Median Annual Income by State 10. 75 80 85 90 95 (Source: U.S. Census Bureau) 11. Archaeology The depths (in inches) at which 10 artifacts are found are listed. 20.7 24.8 30.5 26.2 36.0 34.3 30.3 29.5 27.0 38.5 (a) Find the range of the data set. (b) Change 38.5 to 60.5 and find the range of the new data set. 12. In Exercise 11, compare your answer to part (a) with your answer to part (b). How do outliers affect the range of a data set? Finding Population Statistics In Exercises 13 and 14, find the range, mean, variance, and standard deviation of the population data set. 13.Drunk Driving The number of alcohol-impaired crash fatalities (in thousands) per year from 2010 through 2019 (Source: National Highway Traffic Safety Administration) 10.1 9.9 10.3 10.1 9.9 10.3 11.0 10.9 10.7 10.1
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