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2.15: Chapter 2 Practice

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    50539
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    2.1 Display Data

    An empty graph template for use with this question.
    Figure \(\PageIndex{1}\)

    14.

    Construct a frequency polygon for the following:

    1. Pulse rates for women Frequency
      60–69 12
      70–79 14
      80–89 11
      90–99 1
      100–109 1
      110–119 0
      120–129 1
      Table \(\PageIndex{1}\)
    2. Actual speed in a 30 MPH zone Frequency
      42–45 25
      46–49 14
      50–53 7
      54–57 3
      58–61 1
      Table \(\PageIndex{2}\)
    3. Tar (mg) in nonfiltered cigarettes Frequency
      10–13 1
      14–17 0
      18–21 15
      22–25 7
      26–29 2
      Table \(\PageIndex{3}\)

    15.

    Construct a frequency polygon from the frequency distribution for the 50 highest ranked countries for depth of hunger.

    Depth of hunger Frequency
    230–259 21
    260–289 13
    290–319 5
    320–349 7
    350–379 1
    380–409 1
    410–439 1
    Table \(\PageIndex{4}\)

    16.

    Use the two frequency tables to compare the life expectancy of men and women from 20 randomly selected countries. Include an overlayed frequency polygon and discuss the shapes of the distributions, the center, the spread, and any outliers. What can we conclude about the life expectancy of women compared to men?

    Life expectancy at birth – women Frequency
    49–55 3
    56–62 3
    63–69 1
    70–76 3
    77–83 8
    84–90 2
    Table \(\PageIndex{5}\)
    Life expectancy at birth – men Frequency
    49–55 3
    56–62 3
    63–69 1
    70–76 1
    77–83 7
    84–90 5
    Table \(\PageIndex{6}\)

    17.

    Construct a times series graph for (a) the number of male births, (b) the number of female births, and (c) the total number of births.

    Sex/Year 1855 1856 1857 1858 1859 1860 1861
    Female 45,545 49,582 50,257 50,324 51,915 51,220 52,403
    Male 47,804 52,239 53,158 53,694 54,628 54,409 54,606
    Total 93,349 101,821 103,415 104,018 106,543 105,629 107,009
    Table \(\PageIndex{7}\)
    Sex/Year 1862 1863 1864 1865 1866 1867 1868 1869
    Female 51,812 53,115 54,959 54,850 55,307 55,527 56,292 55,033
    Male 55,257 56,226 57,374 58,220 58,360 58,517 59,222 58,321
    Total 107,069 109,341 112,333 113,070 113,667 114,044 115,514 113,354
    Table \(\PageIndex{8}\)
    Sex/Year 1870 1871 1872 1873 1874 1875
    Female 56,431 56,099 57,472 58,233 60,109 60,146
    Male 58,959 60,029 61,293 61,467 63,602 63,432
    Total 115,390 116,128 118,765 119,700 123,711 123,578
    Table \(\PageIndex{9}\)

    18.

    The following data sets list full time police per 100,000 citizens along with homicides per 100,000 citizens for the city of Detroit, Michigan during the period from 1961 to 1973.

    Year 1961 1962 1963 1964 1965 1966 1967
    Police 260.35 269.8 272.04 272.96 272.51 261.34 268.89
    Homicides 8.6 8.9 8.52 8.89 13.07 14.57 21.36
    Table \(\PageIndex{10}\)
    Year 1968 1969 1970 1971 1972 1973
    Police 295.99 319.87 341.43 356.59 376.69 390.19
    Homicides 28.03 31.49 37.39 46.26 47.24 52.33
    Table \(\PageIndex{11}\)
    1. Construct a double time series graph using a common x-axis for both sets of data.
    2. Which variable increased the fastest? Explain.
    3. Did Detroit’s increase in police officers have an impact on the murder rate? Explain.

    2.6 Skewness and the Mean, Median, and Mode

    66.

    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 \(\PageIndex{2}\)

    67.

    Describe the relationship between the mean and the median of the distribution in Figure \(\PageIndex{2}\).

     

    68.

    Describe the shape 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 in the middle and taper down to the right and left.
    Figure \(\PageIndex{3}\)

    69.

    Describe the relationship between the mode and the median of the distribution in Figure \(\PageIndex{3}\).

    70.

    Are the mean and the median the exact same in the distribution in Figure \(\PageIndex{3}\)? Why or why not?

    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 \(\PageIndex{4}\)

    72.

    Describe the relationship between the mode and the median of the distribution in Figure \(\PageIndex{4}\).

    73.

    Describe the relationship between the mean and the median of the distribution in Figure \(\PageIndex{4}\).

    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 player Batting average Team batting average Team standard deviation
    Fredo 0.158 0.166 0.012
    Karl 0.177 0.189 0.015
    Table \(\PageIndex{12}\)

    82. Use Table \(\PageIndex{12}\) to find the value that is three standard deviations:

    • above the mean
    • below the mean

     

    83.

    Find the standard deviation for the following frequency tables using the formula. 

    1. Grade Frequency
      49.5–59.5 2
      59.5–69.5 3
      69.5–79.5 8
      79.5–89.5 12
      89.5–99.5 5
      Table \(\PageIndex{13}\)
    2. Daily low temperature Frequency
      49.5–59.5 53
      59.5–69.5 32
      69.5–79.5 15
      79.5–89.5 1
      89.5–99.5 0
      Table \(\PageIndex{14}\)
    3. Points per game Frequency
      49.5–59.5 14
      59.5–69.5 32
      69.5–79.5 15
      79.5–89.5 23
      89.5–99.5 2
      Table \(\PageIndex{15}\)

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