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2.15: Chpater 2 Practice

  • Page ID
    51765
  • 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. Pulse rates for womenFrequency
      60–6912
      70–7914
      80–8911
      90–991
      100–1091
      110–1190
      120–1291
      Table \(\PageIndex{40}\)
    2. Actual speed in a 30 MPH zoneFrequency
      42–4525
      46–4914
      50–537
      54–573
      58–611
      Table \(\PageIndex{41}\)
    3. Tar (mg) in nonfiltered cigarettesFrequency
      10–131
      14–170
      18–2115
      22–257
      26–292
      Table \(\PageIndex{42}\)
    15.

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

    Depth of hungerFrequency
    230–25921
    260–28913
    290–3195
    320–3497
    350–3791
    380–4091
    410–4391
    Table \(\PageIndex{43}\)
    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 – womenFrequency
    49–553
    56–623
    63–691
    70–763
    77–838
    84–902
    Table \(\PageIndex{44}\)
    Life expectancy at birth – menFrequency
    49–553
    56–623
    63–691
    70–761
    77–837
    84–905
    Table \(\PageIndex{45}\)
    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/Year1855185618571858185918601861
    Female45,54549,58250,25750,32451,91551,22052,403
    Male47,80452,23953,15853,69454,62854,40954,606
    Total93,349101,821103,415104,018106,543105,629107,009
    Table \(\PageIndex{46}\)
    Sex/Year18621863186418651866186718681869
    Female51,81253,11554,95954,85055,30755,52756,29255,033
    Male55,25756,22657,37458,22058,36058,51759,22258,321
    Total107,069109,341112,333113,070113,667114,044115,514113,354
    Table \(\PageIndex{47}\)
    Sex/Year187018711872187318741875
    Female56,43156,09957,47258,23360,10960,146
    Male58,95960,02961,29361,46763,60263,432
    Total115,390116,128118,765119,700123,711123,578
    Table \(\PageIndex{48}\)
    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.

    Year1961196219631964196519661967
    Police260.35269.8272.04272.96272.51261.34268.89
    Homicides8.68.98.528.8913.0714.5721.36
    Table \(\PageIndex{49}\)
    Year196819691970197119721973
    Police295.99319.87341.43356.59376.69390.19
    Homicides28.0331.4937.3946.2647.2452.33
    Table \(\PageIndex{50}\)
    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.

    2.2 Measures of the Location of the Data

    19.

    Listed are 29 ages for Academy Award winning best actors in order from smallest to largest.Figure \(\PageIndex{15}\)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 \(\PageIndex{16}\)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.

    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 \(\PageIndex{18}\)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:
    • above the mean
    • below the mean

    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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