Ron Larson
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9.3 Describing Dispersion

9.3 Describing Dispersion
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  • 13. Comparing Male and Female SAT Scores

    The histograms show the distributions of SAT scores for mathematics and writing for males and females in a recent year. Describe the differences in the distributions of mathematics SAT scores for males and females. Describe the differences in the distributions of writing SAT scores for males and females. (See Example 5.)

    • Worked-Out Solution

      From the graphs, you can see that males tend to have higher mathematics SAT scores than females. Females tend to have higher writing SAT scores than males.

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      _____    __   __   _    _    __   __    _____   
 / ____||  \ \\/ // | || | ||  \ \\/ //  /  ___|| 
/ //---`'   \ ` //  | || | ||   \ ` //  | // __   
\ \\___      | ||   | \\_/ ||    | ||   | \\_\ || 
 \_____||    |_||    \____//     |_||    \____//  
  `----`     `-`'     `---`      `-`'     `---`
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  • 14. Comparing the Distributions of Mathematics and Writing SAT Scores

    The histograms show the distributions of SAT scores for mathematics and writing for males and females in a recent year. Describe the differences in the distributions of mathematics SAT scores and writing SAT scores for males. Describe the differences in the distributions of mathematics SAT scores and writing SAT scores for females. (See Example 5.)

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               __   __  __    __   __   __            
  ____     \ \\/ // \ \\ / //  \ \\/ //     ___   
 |    \\    \ ` //   \ \/ //    \ ` //     /   || 
 | [] ||     | ||     \  //      | ||     | [] || 
 |  __//     |_||      \//       |_||      \__ || 
 |_|`-`      `-`'       `        `-`'       -|_|| 
 `-`                                         `-`
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  • 15. Analyzing and Explaining a Distribution of SAT Study Hours

    The histogram shows the distribution of the total numbers of hours students at a school study for the SAT over 12 months. What are the two modes of this bimodal distribution? How would you explain the bimodal distribution? (See Example 6.)

    • Worked-Out Solution

      The two peak months that students study more for the SAT are May and October, so May and October are the two modes of this bimodal distribution. Typically, students will take the SAT in May, June, October, or November. This would account for the higher number of study hours in the months before, and the lower number of study hours in January, July, and December.

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     __   _     ______   _    _    __   __   _____    
| || | ||  /_   _// | |  | ||  \ \\/ // |  __ \\  
| '--' ||   -| ||-  | |/\| ||   \ ` //  | |  \ || 
| .--. ||   _| ||_  |  /\  ||    | ||   | |__/ || 
|_|| |_||  /_____// |_// \_||    |_||   |_____//  
`-`  `-`   `-----`  `-`   `-`    `-`'    -----`
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  • 16. Estimating the Percent of Study Hours

    The histogram shows the distribution of the total numbers of hours students at a school study for the SAT over 12 months. What percent of the study hours are in October? (See Example 6)

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      _  __    _____     ______     ___    __    __  
 | |/ //  |  ___||  /_   _//   / _ \\  \ \\ / // 
 | ' //   | ||__    `-| |,-   / //\ \\  \ \/ //  
 | . \\   | ||__      | ||   |  ___  ||  \  //   
 |_|\_\\  |_____||    |_||   |_||  |_||   \//    
 `-` --`  `-----`     `-`'   `-`   `-`     `
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