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9.2 Describing "Average"

9.2 Describing "Average"
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  • 23. Using Mean, Median, and Mode in Advertising Printers

    A consumer testing service is determining the printing speed, in pages per minute (ppm), of three printers. The table shows the results of five print jobs for each printer.

    Each printer has a different manufacturer, and each manufacturer advertises that its printer has a faster average printing speed than its competitors' printers. Which measure of central tendency (mean, median, or mode) would each of the following manufacturers use to support its claim? Explain your reasoning.

    1. the manufacturer of printer A
    2. the manufacturer of printer B
    3. the manufacturer of printer C
    • Worked-Out Solution

      Find and compare the mean, median, and mode of the data for the three manufacturers.

      Printer A: Ordered printing speeds: 27, 28, 30, 32, 32

      Median = 30 ppm (the middle value)

      Mode = 32 ppm (32 occurs twice.)

      Printer B: Ordered printing speeds: 28, 28, 30, 32, 34

      Median = 30 ppm (the middle value)

      Mode = 28 ppm (28 occurs twice.)

      Printer C: Ordered printing speeds: 27, 28, 31, 31, 32

      Median = 31 ppm (the middle value)

      Mode = 31 ppm (31 occurs twice.)

      1. The manufacturer of printer A would use the mode to support its claim, because printer A has the greatest mode of 32 ppm.
      2. The manufacturer of printer B would use the mean to support its claim, because printer B has the greatest mean of 30.4 ppm.
      3. The manufacturer of printer C would use the median to support its claim, because printer C has the greatest median of 31 ppm.
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                 ___      ______   __   __   __   __  
        ___     / _ \\   /_   _//  \ \\/ //  \ \\/ // 
       /   ||  | / \ ||  `-| |,-    \ ` //    \   //  
      | [] ||  | \_/ ||    | ||      | ||     / . \\  
       \__ ||   \___//     |_||      |_||    /_//\_\\ 
        -|_||   `---`      `-`'      `-`'    `-`  --` 
         `-`                                          
    
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  • 24. Using Midrange as a Measure of Central Tendency of Printer Speeds

    A consumer testing service is determining the printing speed, in pages per minute (ppm), of three printers. The table shows the results of five print jobs for each printer.

    The midrange is

    1. Which printer has the fastest average speed according to the midrange?
    2. Why do you think the midrange is rarely used as a measure of central tendency?
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      _  __     ___                _____     _____   
     | |/ //   / _ \\      ___    |  ___||  / ____|| 
     | ' //   / //\ \\    /   ||  | ||__   / //---`' 
     | . \\  |  ___  ||  | [] ||  | ||__   \ \\___   
     |_|\_\\ |_||  |_||   \__ ||  |_____||  \_____|| 
     `-` --` `-`   `-`     -|_||  `-----`    `----`  
                            `-`                      
    
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  • 25. Making a Box-and-Whisker Plot for Printer Prices

    The table below shows the prices of all the printers in stock at an electronics store. Make a box-and-whisker plot of the printer prices.

    • Worked-Out Solution

      Use the Box-and-Whisker Plot Generator located in Tools to make a box-and-whisker plot of the printer prices.

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      _____    _    _    ______      ___      ______  
     / ____|| | || | || |      \\   / _ \\   /_   _// 
    / //---`' | || | || |  --  //  / //\ \\    | ||   
    \ \\___   | \\_/ || |  --  \\ |  ___  ||  _| ||   
     \_____||  \____//  |______// |_||  |_|| /__//    
      `----`    `---`   `------`  `-`   `-`  `--`     
                                                      
    
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  • 26. Describing the Shape of the Distribution of Printer Prices

    The table below shows the prices of all the printers in stock at an electronics store. Describe the shape of the distribution.

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      _____    _    _     ______   _    _    __   _   
     |__  //  | || | ||  /_____// | || | || | || | || 
       / //   | || | ||  `____ `  | || | || | '--' || 
      / //__  | \\_/ ||  /___//   | \\_/ || | .--. || 
     /_____||  \____//   `__ `     \____//  |_|| |_|| 
     `-----`    `---`    /_//       `---`   `-`  `-`  
                         `-`                          
    
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  • 27. Making a Histogram for Printer Prices

    The table below shows the prices of all the printers in stock at an electronics store. Make a histogram of the printer prices.

    • Worked-Out Solution

      Use the Histogram Generator located in Tools to make a histogram of the printer prices.

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       _____     ___      ____      _____             
      / ___//   / _ \\   |  _ \\   |  ___||     ___   
      \___ \\  | / \ ||  | |_| ||  | ||__      /   || 
      /    //  | \_/ ||  | .  //   | ||__     | [] || 
     /____//    \___//   |_|\_\\   |_____||    \__ || 
    `-----`     `---`    `-` --`   `-----`      -|_|| 
                                                 `-`  
    
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  • 28. Describing the Shape of the Distribution of Printer Prices

    The table below shows the prices of all the printers in stock at an electronics store. What new information does the histogram from Exercise 27 give you about the distribution?

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               _    _    _____     _    _      _____  
      ____    | || | || |  __ \\  | || | ||   / ___// 
     |    \\  | || | || | |  \ || | || | ||   \___ \\ 
     | [] ||  | \\_/ || | |__/ || | \\_/ ||   /    // 
     |  __//   \____//  |_____//   \____//   /____//  
     |_|`-`     `---`    -----`     `---`   `-----`   
     `-`                                              
    
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