### 9.3 Describing Dispersion

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• 17. Distribution of Ages for Hodgkin Lymphoma by Rate

The histogram shows the distribution of the ages at which people were diagnosed with Hodgkin lymphoma in a recent year. The table shows the population of the United States for each age group in a recent year. The distribution of the ages is bimodal. How would you explain this?

• Worked-Out Solution

One possible reason may be that children who were not exposed to infectious disease at a young age were more susceptible to the diseases in early adulthood and the diseases were much worse than they would have been if the people had gotten them in childhood. And, for the older mode, it may be related to a weakening of the immune system.

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``` _    _      ___     _____       ___      ______
| \  / ||   / _ \\  |  __ \\    / _ \\   /_____//
|  \/  ||  / //\ \\ | |  \ ||  | / \ ||  `____ `
| .  . || |  ___  ||| |__/ ||  | \_/ ||  /___//
|_|\/|_|| |_||  |_|||_____//    \___//   `__ `
`-`  `-`  `-`   `-`  -----`     `---`    /_//
`-`
```
• 18. Creating a Histogram Using Hodgkin Lymphoma Data

The histogram shows the distribution of the ages at which people were diagnosed with Hodgkin lymphoma in a recent year. The table shows the population of the United States for each age group in a recent year. Use the rates and the populations to create a histogram that estimates the number of people diagnosed with Hodgkin lymphoma for each age group. Is the histogram bimodal? Explain.

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```  ______    ______   __   __    ______    _____
/_____//  /_   _//  \ \\/ //  /_   _//  / ____||
`____ `    -| ||-    \   //    -| ||-  / //---`'
/___//     _| ||_    / . \\    _| ||_  \ \\___
`__ `     /_____//  /_//\_\\  /_____//  \_____||
/_//      `-----`   `-`  --`  `-----`    `----`
`-`
```
• 19. Calculating Standard Deviation (8-Value Data Set)

The formula for the sample standard deviation of a data set is given by

where x represents each value in the data set and n is the number of values in the data set. The symbol ∑ indicates a sum of values. So, is the sum of the data values, and is the sum of the squared data values. Complete the table and then use the formula to find the sample standard deviation of the data set.

• Worked-Out Solution

So, the sample standard deviation of the data set is about 3.3.

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```  _  __    _____      _____     ___     _    _
| |/ //  |  ___||   / ___//   / _ \\  | |  | ||
| ' //   | ||__     \___ \\  | / \ || | |/\| ||
| . \\   | ||__     /    //  | \_/ || |  /\  ||
|_|\_\\  |_____||  /____//    \___//  |_// \_||
`-` --`  `-----`  `-----`     `---`   `-`   `-`

```
• 20. Calculating Standard Deviation (10-Value Data Set)

The formula for the sample standard deviation of a data set is given by

where x represents each value in the data set and n is the number of values in the data set. The symbol Σ indicates a sum of values. So, is the sum of the data values and is the sum of the squared data values. Complete the table and then use the formula to find the sample standard deviation of the data set.

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```           _    _     _____     ______    ______