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5.7.1: Exercises

  • Page ID
    85143
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    1. The table below shows scores on a Math test.

      \(\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|}
      \hline 80 & 50 & 50 & 90 & 70 & 70 & 100 & 60 & 70 & 80 & 70 & 50 \\
      \hline 90 & 100 & 80 & 70 & 30 & 80 & 80 & 70 & 100 & 60 & 60 & 50 \\
      \hline
      \end{array}\)

      1. Complete a frequency table for the Math test scores.
      2. Construct a bar graph of the data.  Label both axes.
      3. Construct a pie chart of the data.  Label the sectors.
    2. A group of adults where asked how many cars they had in their household. Their responses are listed below.

      \(\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|}
      \hline 1 & 4 & 2 & 2 & 1 & 2 & 3 & 3 & 1 & 4 & 2 & 2 \\
      \hline 1 & 2 & 1 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 2 \\
      \hline
      \end{array}\)

      1. Complete a frequency table for the number of cars data.
      2. Construct a bar graph of the data.  Label the axes.
      3. Construct a Pareto chart of the data.  Label the axes.
      4. Construct a pie chart of the data.  Label the sectors.
    3. dd25.svgA group of adults were asked how many children they have in their families. The bar graph to the right shows the number of adults who indicated each number of children.
      1. How many adults where questioned?
      2. What percentage of the adults questioned had 0 children?
      3. Create a pie graph for the number of children in these families.  Label the sectors.
    4. Jasmine was interested in how many days it would take an order from Amazon to arrive at her door. The graph below shows the data she collected.

      dd26.svg

      1. How many items did she order?
      2. What percentage of the items arrived in one day?
      3. Create a pie graph for her data.  Label the sectors.
    5. The bar graph below shows the percentage of students who received each letter grade on their last English paper. The class contains 20 students. What number of students earned an A on their paper?

      dd27.svg

      1. How many students earned an A on their papers?
      2. Create a frequency bar graph for these data.  How do the two bar graphs compare?
    6. Kori categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The percents she spent in each category are pictured here. If she spent a total of $2600 this month, how much did she spend on rent?

      dd28.svg

    7. 50 people were asked about the number of television sets in their houses.  The pie chart below shows their responses.

      Screen Shot 2021-10-31 at 2.56.41 PM.jpg

      1. How many television sets did the largest number of people have?
      2. How many television sets did the fewest number of people have?
      3. How many people had no television sets?
      4. How many people had at least 3 television sets?
      5. What percent of the people surveyed had at most 2 television sets?
      6. How many people had not more than 2 television sets? 
    8. In 2018, 487,890 people in California graduated from college with various degrees.  The numbers are shown in the chart below.
      Associate's Degree 170,890
      Bachelor's Degree 216,810
      Master's Degree 80,480
      Doctorate or Professional Degree 19,710
      1. Is the data categorical or numerical?
      2. Which type(s) of graphs would be appropriate way(s) to display this information? Bar Graph, Pareto Chart, Pie Chart, Frequency Histogram, or Frequency Polygon
    9. The ages of the U.S.Presidents who were inaugurated in the 20th century are given.

      42; 51; 56; 55; 51; 54; 51; 60; 62; 43; 55; 56; 61; 52; 69; 64; 46

      1. Create a grouped frequency table for these scores starting at 40 with a class width of 10.
      2. Create a frequency histogram for these scores.
      3. Describe the shape of the frequency histogram.
    10. Results for 40 students on a recent math exam are given.

      83; 76; 98; 75; 56; 47; 67; 92; 69; 74; 72; 84; 96; 66; 51; 64; 58; 80; 85; 78; 58; 88; 90; 76; 74; 82; 76; 66; 50; 84; 66; 79; 83; 43; 54; 93; 77; 67; 54; 76

      1. Create a grouped frequency table for these scores starting at 40 with a class width of 10.
      2. Create a frequency histogram for these scores.
      3. Describe the shape of the frequency histogram.
      4. Make a frequency polygon for this data.
    11. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average length of time in months patients live once starting the treatment. A researcher follows a set of 40 AIDS patients from the start of treatment until their deaths. The following data (in months) are collected.

      3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 34

      1. Create a frequency table starting at 0 with a class width of 6 months.
      2. What percent of the AIDS patients in the study survived at least 3 years after beginning treatment?
      3. What percent of the AIDS patients in the study survived less than 18 months?
      4. Create a frequency histogram using the above data.  Label the axes.
    12. As part of a study, the weights of 42 medium-sized dogs were measured in pounds.  The results are shown below.
      26.1 16.2 21.1 34.7 45.3 18.5 41.6
      38.8 22.9 48.1 27.1 22.4 30.6 39.1
      62.8 25.1 25.0 38.6 29.9 31.7 28.9
      20.3 56.1 60.5 24.0 61.7 28.6 32.9
      33.5 18.0 23.5 27.9 46.8 30.0 34.3
      62.2 49.3 59.7 19.6 20.8 23.2 24.4
      1. Create a frequency table using classes. Start at 16 and use a class width of 8.
      2. What percent of the dogs weigh no more than 24 pounds?
      3. What percent of the dogs studied weigh at least 48 pounds?
      4. What percent of the dogs studied weigh at least 24 pounds, but do not exceed 40 pounds?
    13. People were asked how long they waited in line to ride a popular attraction at a local theme park.  The frequency table below shows the results.
      x = Time (minutes) Frequency
      0 ≤ x < 5 32
      5 ≤ x < 10 47
      10 ≤ x < 15 36
      15 ≤ x < 20 22
      20 ≤ x < 25 13
      25 ≤ x < 30 10
      1. Construct a histogram to represent the data.  Label the axes of your histogram.
      2. Describe the shape of the histogram.
    14. Hourly wages of workers at a local company are shown in the frequency table below.
      x = Hourly Wage (dollars) Frequency
      13.00 ≤ x < 14.50 21
      14.50 ≤ x < 16.00 35
      16.00 ≤ x < 17.50 42
      17.50 ≤ x < 19.00 27
      19.00 ≤ x < 20.50 18
      20.50 ≤ x < 22.00 9
      1. Construct a histogram to represent the data.  Label the axes of your histogram.
      2. Describe the shape of the histogram.
    15. The frequency histogram below shows the number of hours per day a random sample of teenagers spent watching television.

      Student TV Histogram.jpg

      1. How many teenagers were included in the sample?
      2. What percent of the teenagers in the sample spent less than 4 hours watching television?
      3. What percent of the teenagers in the sample spent at least 5 hours watching television?
      4. What percent of the teenagers in the sample spent at least 1 hour watching television?
      5. What percent of the teenagers in the sample spent less than 2 hours watching television?
      6. What percent of the teenagers in the sample spent at least 2 hours but less than 4 hours watching television?
      7. What percent of the teenagers in the sample spent more than 3.5 hours watching television?
    16. A pet food company is testing the accuracy of the machine that fills its boxes with bird food.  The weights of the sample boxes are shown in the frequency histogram.

      Weights of Bird seed boxes.jpg

      1. How many boxes did the company test?
      2. How many of the boxes tested weighed at least 16.1 ounces?
      3. What percent of the boxes tested weighed less than 15.9 ounces?
      4. What percent of the boxes tested weighed within 0.1 ounces of the 16 ounce weight stated on the box?  That is,15.9 ≤ w < 16.1 where w is the weight of the box.
      5. If boxes weighing within 0.1 ounces of the 16-ounce stated weight are acceptable, are there more underweight boxes or overweight boxes among the boxes that do not meet the weight standard?

    This page titled 5.7.1: Exercises is shared under a not declared license and was authored, remixed, and/or curated by Leah Griffith, Veronica Holbrook, Johnny Johnson & Nancy Garcia.

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