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2.14: Chapter Practice

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    2.1 Display Data

    An empty graph template for use with this question.
    Figure \(\PageIndex{14}\)
    14.

    Construct a frequency polygon for the following:

    1. Describe the relationship between the mode and the median of this distribution.
      This is a histogram which consists of 5 adjacent bars with the x-axis split into intervals of 1 from 3 to 7. The bar heights peak at the first bar and taper lower to the right. The bar ehighs from left to right are: 8, 4, 2, 2, 1.
      Figure \(\PageIndex{16}\)
      67.

      Describe the relationship between the mean and the median of this distribution.

      This is a histogram which consists of 5 adjacent bars with the x-axis split into intervals of 1 from 3 to 7. The bar heights peak at the first bar and taper lower to the right. The bar heights from left to right are: 8, 4, 2, 2, 1.
      Figure \(\PageIndex{17}\)
      68.

      This is a histogram which consists of 5 adjacent bars with the x-axis split into intervals of 1 from 3 to 7. The bar heights peak in the middle and taper down to the right and left.
      Figure \(\PageIndex{18}\)
      69.

      Describe the relationship between the mode and the median of this distribution.

      This is a histogram which consists of 5 adjacent bars with the x-axis split intervals of 1 from 3 to 7. The bar heights peak in the middle and taper down to the right and left.
      Figure \(\PageIndex{19}\)
      70.

      Are the mean and the median the exact same in this distribution? Why or why not?

      This is a histogram which consists of 5 adjacent bars with the x-axis split into intervals of 1 from 3 to 7. The bar heights from left to right are: 2, 4, 8, 5, 2.
      Figure \(\PageIndex{20}\)
      71.

      Describe the shape of this distribution.

      This is a histogram which consists of 5 adjacent bars over an x-axis split into intervals of 1 from 3 to 7. The bar heights from left to right are: 1, 1, 2, 4, 7.
      Figure \(\PageIndex{21}\)
      72.

      Describe the relationship between the mode and the median of this distribution.

      This is a histogram which consists of 5 adjacent bars over an x-axis split into intervals of 1 from 3 to 7. The bar heights from left to right are: 1, 1, 2, 4, 7.
      Figure \(\PageIndex{22}\)
      73.

      Describe the relationship between the mean and the median of this distribution.

      This is a histogram which consists of 5 adjacent bars over an x-axis split into intervals of 1 from 3 to 7. The bar heights from left to right are: 1, 1, 2, 4, 7.
      Figure \(\PageIndex{23}\)
      74.

      The mean and median for the data are the same.

      3; 4; 5; 5; 6; 6; 6; 6; 7; 7; 7; 7; 7; 7; 7

      Is the data perfectly symmetrical? Why or why not?

      75.

      Which is the greatest, the mean, the mode, or the median of the data set?

      11; 11; 12; 12; 12; 12; 13; 15; 17; 22; 22; 22

      76.

      Which is the least, the mean, the mode, and the median of the data set?

      56; 56; 56; 58; 59; 60; 62; 64; 64; 65; 67

      77.

      Of the three measures, which tends to reflect skewing the most, the mean, the mode, or the median? Why?

      78.

      In a perfectly symmetrical distribution, when would the mode be different from the mean and median?

      2.7 Measures of the Spread of the Data

      Use the following information to answer the next two exercises: The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles.
      29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150

      79.

      Use a graphing calculator or computer to find the standard deviation and round to the nearest tenth.

      80.

      Find the value that is one standard deviation below the mean.

      81.

      Two baseball players, Fredo and Karl, on different teams wanted to find out who had the higher batting average when compared to his team. Which baseball player had the higher batting average when compared to his team?

      Baseball playerBatting averageTeam batting averageTeam standard deviation
      Fredo0.1580.1660.012
      Karl0.1770.1890.015
      Table 2:59 to find the value that is three standard deviations:
      • Find the standard deviation for the following frequency tables using the formula. Check the calculations with the TI 83/84.83.

        Find the standard deviation for the following frequency tables using the formula. Check the calculations with the TI 83/84.

        1. GradeFrequency
          49.5–59.52
          59.5–69.53
          69.5–79.58
          79.5–89.512
          89.5–99.55
          Table \(\PageIndex{60}\)
        2. Daily low temperatureFrequency
          49.5–59.553
          59.5–69.532
          69.5–79.515
          79.5–89.51
          89.5–99.50
          Table \(\PageIndex{61}\)
        3. Points per gameFrequency
          49.5–59.514
          59.5–69.532
          69.5–79.515
          79.5–89.523
          89.5–99.52
          Table \(\PageIndex{62}\)

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