8.5.2: Exercise 2.4-W Picturing Health Care Data with Graphs

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    MAKING CONNECTIONS TO THE COLLABORATION

    (1) Which of the following was one of the main mathematical ideas of the collaboration?


    Circle graph showing Graph A, indicating the following: Part A1 = Smaller portion Part A2 = Larger portion Circle graph showing Graph B, indicating the following: Part B1 = Smaller portion Part B2 = Larger portion

    (i) It is important to monitor your calorie intake for a healthy diet.

    (ii) In Graph A above, you can find the quantity represented by “Part A1” by multiplying the percentage for the section times the total quantity represented by the circle.

    (iii) In the graphs above, you know that “Part A2” represents a larger quantity than “Part B2” because the piece of the graph is larger.

    (iv) In the graphs above, you cannot compare the quantities represented by the parts because you do not know the reference values.

    DEVELOPING SKILLS AND UNDERSTANDING

    (2) Use the graph8 below to answer the following questions. (Note: The median is the middle number of a data set when the numeric values are arranged in order of size.)

    Line graph showing the Median New House Cost in the United States annual data from 2002 to 2014. Y-axis represents the prices, ranging from $180,000 to $280,000. X-axis represents the years, ranging from 2002 to 2014. 2003 = in between $180,000 and $200,000 2004 = in between $200,000 and $220,000 2005 = in between $220,000 and $240,000 2006 = in between $240,000 and $260,000 2007 = in between $240,000 and $260,000 2008 = in between $220,000 and $240,000 2009 = in between $200,000 and $220,000 2010 = in between $220,000 and $240,000 2011 = in between $220,000 and $240,000 2012 = in between $240,000 and $260,000 2013 = in between $260,000 and $280,000 2014 = in between $260,000 and $280,000

    (a) Estimate the percentage increase in new housing prices from 2003 to 2007. (Choose the best answer.)

    (i) The prices increased from around $190,000 to around $245,000, about a 29% increase.

    (ii) The prices increased from around $190,000 to around $220,000, about a 16% increase.

    (iii) The prices increased from around $190,000 to around $245,000, about a 22% increase.

    (iv) The prices increased from around $190,000 to around $220,000, about a 14% increase.

    (b) Estimate the percentage increase in new housing prices from 2011 to 2013. (Fill in the blanks.)

    The prices increased from ___________ to ___________. This is about a ________% increase.

    (c) Estimate the percentage decrease from 2007 to 2009. (Fill in the blanks.)

    The prices decreased from ___________ to __________. This is about a ________% decrease.

    (3) South Central Bank has a policy that limits the amount of debt customers may have in order to receive a loan. The following pie chart shows the highest percentage of debt that the bank will allow.

    Circle graph showing the South Central Bank has a policy that limits the amount of debt customers. Debt = 36% Other Expenses = 64%

    (a) What is the reference value in this situation?

    (i) Other expenses

    (ii) Debt

    (iii) Total of other expenses and debt

    (iv) Other expenses minus debt

    (b) Three graphs are given below. Each graph represents a loan customer. Each customer’s debt is broken into three categories: car, credit card, and mortgage (the loan on a house). Which customer(s) meet the bank policy on the limit of the amount of debt? There may be more than one correct answer.

    (i)

    (ii)

    Circle graph showing the Customer A. Car = 4% Credit Card = 2% Mortgage = 30% Other Expenses = 64%

    Circle graph showing the Customer B. Car = 8% Credit Card = 4% Mortgage = 35% Other Expenses = 53%


    (iii)

    Circle graph showing the Customer C. Car = 5% Credit Card = 5% Mortgage = 10% Other Expenses = 80%

    (4) The pie charts below present data about obesity in the U.S.9 The population of the United States in 2005 was approximately 296 million people. In 2050, the U.S. population is predicted to be 439 million. Use this information to answer the questions below.

    Circle graph showing Projected obesity in the U.S. for 2050. Obese = 42% Non-obese = 58%

    Circle graph showing obesity in the U.S. for 2005. Obese = 23% Non-obese = 77%

    (a) Calculate the number of non-obese people in the U.S. in 2005. Round your answer to the nearest million.

    (b) Calculate the projected number of the non-obese people in the U.S. 2050. Round your answer to the nearest million.

    (c) What is the change in the number of non-obese people in the U.S. from 2005 to 2050 in relative terms?

    (d) What is the change in the number of non-obese people in the U.S. from 2005 to 2050 in absolute terms?

    MAKING CONNECTIONS ACROSS THE COURSE

    (5) From 2000 to 2006, a total of 19,076 teens (ages 15–19) were killed in car crashes in the United States. The number of teen males who were killed was 12,479 and the number of teen females who were killed was 6,597.10

    A reporter used this information to write, “About 34%, or one out of every three girls will be killed in a car crash.” Which of the following statements is the best critique of this statement?

    (i) The statement is correct because 6,597 is 34% of 19,076, which is very close to one-third. The ratio of 1 out of 3 is a good estimate of the percentage.

    (ii) The statement is incorrect because 6,597 is 34% of 19,076, which is very close to three-tenths. The ratio of 1 out of 3 is not a good estimate of the percentage.

    (iii) The statement is incorrect because the reference value is the number of teens killed, not all teen girls. It would be correct to say that 34% of teens killed in car crashes are female.

    (iv) The statement is incorrect because 6,597 is about 50% of 12,479. The ratio of 1 out of 3 is not a good estimate of the percentage.

    (6) The following graphs show how much two families spend on tickets to professional baseball games each year.

    Vertical bar graph showing how much two families spend on tickets to professional baseball games in 2010. Y-axis represents the amount, ranging from $0 to $7,000. X-axis represents each family. Cobb family = $6,000 Wagner family = in between $1,000 and $2,000
    Vertical bar graph showing how much two families spend on tickets to professional baseball games in 2010 (percent of income). Y-axis represents the percentage, ranging from 0% to 6%. X-axis represents each family. Cobb family = 3% Wagner family = 5%

    Choose the true statement based on these graphs.

    (i) The Wagners must have a higher income than the Cobbs. They spend less on baseball tickets, but it is a higher portion of their total income.

    (ii) The Cobbs must have a higher income than the Wagners. They spend more on baseball tickets, but it is a smaller portion of their total income.

    (iii) The Wagners must have a higher income than the Cobbs. They spend more on baseball tickets, but it is a smaller portion of their total income.

    (iv) The Cobbs must have a lower income than the Wagners. They spend more on baseball tickets, but it is a smaller portion of their total income.

    _________________________________

    8 https://www.census.gov/construction/nrs/pdf/uspricemon.pdf

    9 http://news.harvard.edu/gazette/story/2010/11/obesity-rate-will-reach-at-least-42/

    10 http://www.cdc.gov/MotorVehicleSafety/Teen_Drivers/data.html

    This page titled 8.5.2: Exercise 2.4-W Picturing Health Care Data with Graphs was last modified on Wed, 15 May 2024 07:37:27 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Carnegie Math Pathways (WestEd) .