Pie chart on monthly expenses of a family

Lesson 2.8

Introduction

Course Objectives

This lesson will address the following course outcomes:

· 7. Read, interpret, and make decisions based upon data from tables and graphical displays such as line graphs, bar graphs, scatterplots, pie charts, and histograms. Given data, choose an appropriate type of graphical display and create it using scales appropriate to the application.

Specific Objectives

Students will understand that

· the scale on graphs can change perception of the information they represent.

· to fully understand a pie graph, the reference value must be known.

Students will be able to

· calculate relative change from a line graph.

· estimate the absolute size of the portions of a pie graph given its reference value.

· use data displayed on two graphs to estimate a third quantity.

Graphs are a helpful way to summarize data. Often there are many ways to portray information graphically. Sometimes one form is easier to read than another. Sometimes the way a graph is made can affect the impression it gives. Today, you will look at three examples of such graphs.

Line Graphs

Problem Situation 1: Reading Line Graphs

#1 Points possible: 5. Total attempts: 5

Compare the two graphs below.

https://s3.amazonaws.com/wamapdata/ufiles/2/QW2-1-3-1a.JPG https://s3.amazonaws.com/wamapdata/ufiles/2/QW2-1-3-1b.JPG

Which statement best descries the relationship between the graphs?

· The data appears to be different - the first graph shows larger changes in income

· They appear to show the same data, but on different vertical scales.

#2 Points possible: 5. Total attempts: 5

What was the average household income in 1999?

$

#3 Points possible: 5. Total attempts: 5

Based on these two graphs, would it be fair to say that the average household income was significantly lower in 2009 than it was in 1999?

Give your answer with an explanation, then compare your answer to the one provided.

Bar Graphs

Problem Situation 2: Reading Bar Graphs

In this example, we will be looking at bar graphs. Before doing that, answer the question about Jeff’s Housing so that you can understand the questions about national debt and GDP that follow.

#4 Points possible: 15. Total attempts: 5

Jeff’s Housing: Two pairs of statements are given below.

In 1990, Jeff spent $1,000 per month on housing. In 2010, Jeff spent $2,000 per month on housing.

In 1990, Jeff spent 20% of his income on housing. In 2010, Jeff spent 10% of his income on housing.

a. How can both pairs of statements be true?

· It is not possible for both statements to be true, since one shows his housing costs rising, and the other shows his housing costs decreasing

· Both statements can be true if his income increased significantly from 1990 to 2010

· Both statements can be true if his income fell significantly from 1990 to 2010

b. Calculate Jeff's monthly income in 1990 $

c. Calculate Jeff's monthly income in 2010 $

GDP, or Gross Domestic Product, can be thought of as the country’s income. It is the value of all goods and services the country produces. The national debt is how much the country owes. Just as Jeff’s spending on housing can be calculated as a percent of income, a country’s national debt can be calculated as a percent of its GDP.

https://s3.amazonaws.com/wamapdata/ufiles/2/QW2-1-3-3a.JPG https://s3.amazonaws.com/wamapdata/ufiles/2/QW2-1-3-3b.JPG

#5 Points possible: 10. Total attempts: 5

Using the graphs above,

a) What was the national debt in 2010?

trillion dollars

b) What percent of the GDP was the national debt in 2010?

%

#6 Points possible: 5. Total attempts: 5

Consider the two graphs above.

Think about the statement, "The 2010 national debt is way out of hand and has never been higher." Use the graphs above to evaluate the statement. While of the following is most correct?

· The total debt has never been higher, but as a percentage of income debt was not at the highest level ever in 2010

· The debt is higher than the last few decades, but was higher in 1950

· The debt has never been higher

· As a percentage of GDP, debt is higher now than in the last few decades, but it was higher in 1950

Pie Graphs

Problem Situation 3: Reading Pie (Circle) Graphs

#7 Points possible: 5. Total attempts: 5

Decide if the following statement is true or false based on the two graphs below.

https://s3.amazonaws.com/wamapdata/ufiles/2/M96L28g3.PNG

True or False: This pair of graphs predicts that the number of non-Hispanics in the United States is expected to decline between 2010 and 2050.

· True

· False

· Not enough information is given

#8 Points possible: 10. Total attempts: 5

The U.S. population in 2010 was around 310,000,000. In 2050, the U.S. population is expected to be around 439,000,000. Using this information and the pie charts above, find the number of non-Hispanic Americans at each time, to the nearest million people.

Non-Hispanic Americans in 2010: million people

Non-Hispanic Americans in 2050: million people

#9 Points possible: 5. Total attempts: 5

Based on your calculations, now what can you conclude about this statement?

True or False: This pair of graphs predicts that the number of non-Hispanics in the United States is expected to decline between 2010 and 2050.

· True

· False

· Not enough information is given

HW 2.8

#1 Points possible: 5. Total attempts: 5

Which of the following was one of the main mathematical ideas of the lesson?

· In the graphs below, you know that Part A2 represents a larger quantity than Part B2 because the piece of the graph is larger.

· In Graph A, you can find the quantity represented by Part A1 by multiplying the percentage for the section times the total quantity represented by the circle.

· It is important to consider the gross national product when considering the size of the national debt. They relate to each other just as a person's personal debt relates to his/her income.

· In the graphs below, you must know the reference values to compare the quantities represented by the parts A1 and A2.

https://wamaps3.s3.amazonaws.com/qimages/2.1.4.1a.PNG https://wamaps3.s3.amazonaws.com/qimages/2.1.4.1b.PNG

#2 Points possible: 14. Total attempts: 5

Use the graph below to answer the following questions.1

https://wamaps3.s3.amazonaws.com/qimages/QW2143.JPG

a. Estimate the percentage increase in new housing prices from 1999 to 2007. (Choose the best answer.)

· The prices increased from around $160,000 to around $245,000, about a 65% increase.

· The prices increased from around $160,000 to around $220,000, about a 35% increase.

· The prices increased from around $160,000 to around $220,000, about a 38% increase.

· The prices increased from around $160,000 to around $245,000, about a 53% increase.

b. Estimate the percentage increase in new housing prices from 2004 to 2007. (Fill in the blanks.) The prices increased from $ to $. This is about an 12% 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 Points possible: 10. Total attempts: 5

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.

https://wamaps3.s3.amazonaws.com/qimages/2.1.4.4.PNG

a. What is the reference value in this situation?

· Other expenses

· Debt

· Total of other expenses and debt

· None of the above

b. Three graphs are given below. Each graph represents a loan customer. The customers’ 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.

· https://wamaps3.s3.amazonaws.com/qimages/2.1.4.4a.PNG

· https://wamaps3.s3.amazonaws.com/qimages/2.1.4.4b.PNG

· https://wamaps3.s3.amazonaws.com/qimages/2.1.4.4c.PNG

#4 Points possible: 5. Total attempts: 5

In Lesson 1.9, you used results from the 2009 Consumer Expenditure Survey on how Americans spend their income. A summary of this information is given in Table 12.

Table 1: Percentages of Average Annual Housing Expenditures

Housing

34.43%

Food

12.99%

Transportation

15.61%

Everything Else

36.97%

Which pie graph best represents the data given in Table 1?

· https://wamaps3.s3.amazonaws.com/qimages/2.1.3.8d.png

· https://wamaps3.s3.amazonaws.com/qimages/2.1.3.8c.png

· https://wamaps3.s3.amazonaws.com/qimages/2.1.3.8a.png

· https://wamaps3.s3.amazonaws.com/qimages/2.1.3.8b.png

#5 Points possible: 20. Total attempts: 5

The following two pie graphs show how two families spend their money. The Alvarez family has a take-home pay of $3,650 per month and the Martinez family has a take-home pay of $7,300 per month.

https://wamaps3.s3.amazonaws.com/qimages/QW2145.JPG

a. Select the statement that best compares how much the families spend on gasoline.

· The Alvarez family spent more on gasoline than the Martinez family because 3% of $7,300 is more than 6% of $3,650.

· The two families both spent $200 on gasoline.

· The Alvarez Family spent more on gasoline than the Martinez Family.

· Both families spend around $200 on gasoline. This is 6% of the Alvarez budget, but only 3% of the Martinez budget because the Martinez family starts with about twice as much money as the Alvarez family.

b. Estimate the actual spending on food and housing for each family. (Fill in the tables. Be sure to estimate - exact answers are not accepted.)

Alvarez Family

Food

$

Housing

$

c.

Martinez Family

Food

$

Housing

$

d.

e. Both families spend about the same percentage of their income on housing. The family with the income can afford a house that has twice the payment and maintenance costs.

#6 Points possible: 10. Total attempts: 5

The Center for Disease Control (CDC) published the following information about respiratory disease in children. Respiratory disease is an illness that affects a person’s ability to breathe and use oxygen.3

In 2005, approximately one fourth of the 2.4 million hospitalizations for children aged < 15 years were for respiratory diseases, the largest category of hospitalization diagnoses in this age group. Of these, 31% were for pneumonia, 25% for asthma, 25% for acute bronchitis and bronchiolitis, and 19% for other respiratory diseases, including croup and chronic disease of tonsils and adenoids.

a. Based on this information, how many children were hospitalized for pneumonia in 2005? children

b. Which of the following pie charts accurately represents the data for children hospitalized for respiratory diseases?

https://s3.amazonaws.com/wamapdata/ufiles/2/4-1-5-8a.jpg https://s3.amazonaws.com/wamapdata/ufiles/2/4-1-5-8b.jpg https://s3.amazonaws.com/wamapdata/ufiles/2/4-1-5-8c.jpg

#7 Points possible: 5. Total attempts: 5

A group of adults were asked how many children they have in their families. The bar graph below shows the number of adults who indicated each number of children. 1234567Number of Children012345 How many adults were questioned? What percentage of the adults questioned had 0 children? %

#8 Points possible: 5. Total attempts: 5

Jan23Feb21Mar16Apr12May9Jun7July5Aug7Sept9Oct12Nov16Dec10MillimetersAverage Monthly Precipitation010203040 Using the bar graph from above to answer the following questions: a)The average monthly precipitation in February is how many times the average monthly precipitation in June? b) The average monthly precipitation in December is how many times the average monthly precipitation in July?