📚 Math in Society
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11.6 Exercises

Skills

  1. The table below shows scores on a Math test.
    1. Complete the frequency table for the Math test scores
    2. Construct a histogram of the data
    3. Construct a pie chart of the data

8050509070701006070807050
90100807030808070100606050

  1. A group of adults where asked how many cars they had in their household
    1. Complete the frequency table for the car number data
    2. Construct a histogram of the data
    3. Construct a pie chart of the data

142212331422
121322121112

  1. Bar graph with the horizontal axis Number of children marked 0 to 5 and the vertical axis Frequency marked 0 to 6. The bar at 0 children reaches 5 adults, at 1 child 3 adults, at 2 children 4 adults, at 3 children 2 adults, there is no bar at 4 children, and at 5 children the bar reaches 1 adult.A 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?
  1. Jasmine was interested in how many days it would take an order from Netflix to arrive at her door. The graph below shows the data she collected.
    1. How many movies did she order?
    2. What percentage of the movies arrived in one day?
Bar graph of how long Netflix orders took to arrive. Horizontal axis Shipping time (days) with labels 1 to 5, vertical axis Frequency 0 to 8 with gridlines. Heights: 1 day 4, 2 days 8, 3 days 6, 4 days none, 5 days 1, so 19 movies in all.
  1. 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?
Bar chart of the percentage of a 20-student class earning each letter grade on an English paper. The vertical axis is Frequency (%) from 0 to 40 in steps of 10 with gridlines; the horizontal axis carries the category labels A, B, C and D but is mistitled Number of children. Heights: A 25 percent, B 35 percent, C 25 percent, D 15 percent.
  1. 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?
Pie chart of one month's spending in four categories, each slice labelled with its name and percent, reading clockwise from the top: Food 24 percent, Rent 26 percent, Other 34 percent, Fun 16 percent.
  1. A group of diners were asked how much they would pay for a meal. Their responses were: $7.50, $8.25, $9.00, $8.00, $7.25, $7.50, $8.00, $7.00.
    1. Find the mean
    2. Find the median
    3. Write the 5-number summary for this data
    4. Find the standard deviation of this data
  1. You recorded the time in seconds it took for 8 participants to solve a puzzle. The times were: 15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, 29.4.
    1. Find the mean
    2. Find the median
    3. Write the 5-number summary for this data
    4. Find the standard deviation of this data
  1. Refer back to the histogram from question #3.
    1. Compute the mean number of children for the group surveyed
    2. Compute the median number of children for the group surveyed
    3. Write the 5-number summary for this data.
    4. Create box plot.
  1. Refer back to the histogram from question #4.
    1. Compute the mean number of shipping days
    2. Compute the median number of shipping days
    3. Write the 5-number summary for this data.
    4. Create box plot.

Concepts

  1. The box plot below shows salaries for Actuaries and CPAs. Kendra makes the median salary for an Actuary. Kelsey makes the first quartile salary for a CPA. Who makes more money? How much more?
Two stacked boxplots comparing salaries on a shared horizontal axis labelled Salary (thousands of $) running from 30 to about 105. No values are printed, so these are read off the scale. CPA, on top: minimum 30, first quartile 40, median 75, third quartile 90, maximum about 99. Actuary, below: minimum 40, first quartile 75, median 90, third quartile about 95, maximum about 105.
  1. Referring to the boxplot above, what percentage of actuaries makes more than the median salary of a CPA?

Exploration

  1. Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. 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. Two researchers each follow a different set of 40 AIDS patients from the start of treatment until their deaths. The following data (in months) are collected.

Researcher 1: 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

Researcher 2: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29

  1. Create comparative histograms of the data
  2. Create comparative boxplots of the data
  1. A graph appears below showing the number of adults and children who prefer each type of soda. There were 130 adults and kids surveyed. Discuss some ways in which the graph below could be improved
Comparative 3-D bar chart of soda preference among about 130 kids and about 130 adults, with a legend marking Kids in pale cyan and Adults in dark blue. The vertical axis carries no label at all and starts at 20 rather than 0, ending at 45. Reading the bar tops against the gridlines: Coke about 44 kids and 30 adults, Diet Coke about 22 kids and 37 adults, Sprite about 32 kids and 36 adults, Cherry Coke about 33 kids and 27 adults. The unlabelled axis, the baseline at 20 and the slanted 3-D block tops all make the values hard to read, which is what the exercise asks about.
  1. Make up three data sets with 5 numbers each that have:
    1. the same mean but different standard deviations.
    2. the same mean but different medians.
    3. the same median but different means.
  1. A sample of 30 distance scores measured in yards has a mean of 7, a variance of 16, and a standard deviation of 4.
    1. You want to convert all your distances from yards to feet, so you multiply each score in the sample by 3. What are the new mean, median, variance, and standard deviation?
    2. You then decide that you only want to look at the distance past a certain point. Thus, after multiplying the original scores by 3, you decide to subtract 4 feet from each of the scores. Now what are the new mean, median, variance, and standard deviation?
  1. In your class, design a poll on a topic of interest to you and give it to the class.
    1. Summarize the data, computing the mean and five-number summary.
    2. Create a graphical representation of the data.
    3. Write several sentences about the topic, using your computed statistics as evidence in your writing.

Adapted from Math in Society by David Lippman, hosted on LibreTexts (math.libretexts.org) and licensed under CC BY-SA 3.0. Changes were made. License: CC-BY-SA-3.0.

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