Prealgebra

Alan S. Tussy, R. David Gustafson, Diane R. Koenig

Chapter 8

Graphs and Statistics - all with Video Answers

Educators

Section 1

Reading Graphs and Tables

Problem 1

Refer to graphs a through f below. Fill in the blanks with the correct letter.
Graph _____ is a bar graph.
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 2

Refer to graphs a through f below. Fill in the blanks with the correct letter.
Graph is a circle graph.
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 3

Refer to graphs a through f below. Fill in the blanks with the correct letter.
Graph is a pictograph.
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 4

Refer to graphs a through f below. Fill in the blanks with the correct letter.
Graph is a line graph.
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 5

Refer to graphs a through f below. Fill in the blanks with the correct letter.
Graph is a histogram.
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 6

Refer to graphs a through f below. Fill in the blanks with the correct letter.
Graph is a frequency polygon.
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 7

A horizontal or vertical line used for reference in a bar graph is called an _____ .

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 8

In a circle graph, slice-of-pie–shaped figures called _____ are used to show what part of the whole each quantity represents.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 9

Fill in the blanks.
To read a table, we must find the _____ of the row and column that contains the desired information.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 10

Fill in the blanks.
The _____ axis and the vertical axis of a bar graph serve to frame the graph, and they are scaled in units such as years, dollars, minutes, pounds, and percent.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 11

Fill in the blanks.
A pictograph is like a bar graph, but the bars are made from _____ or symbols.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 12

Fill in the blanks.
Line graphs are often used to show how a quantity changes with . On such graphs, we can easily see when a quantity is increasing and when it is _____.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 13

Fill in the blanks.
A histogram is a bar graph with three important features.
$\cdot$ The _____ of a histogram touch.
$\cdot$ Data values never fall at the _____ of a bar.
$\cdot$ The widths of the bars of a histogram are _____ and represent a range of values.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 14

Fill in the blanks.
A frequency polygon can be constructed from a histogram by joining the _____ points at the top of each bar.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 15

If the symbol CAN'T COPY THE IMAGE =1,000 buses, estimate what the symbol CAN'T COPY THE IMAGE represents.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 16

Fill in the blank: The symbol CAN'T COPY THE SYMBOL is used when graphing to show a _____ in the scale on an axis.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 17

Find the cost of using priority mail to send a package weighing $7 \frac{1}{4}$ pounds to zone 3

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 18

Find the cost of sending a package weighing $2 \frac{1}{4}$ pounds to zone 5 by priority mail.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 19

A woman wants to send a birthday gift and an anniversary gift to her brother, who lives in zone 6 using priority mail. One package weighs 2 pounds 9 ounces, and the other weighs 3 pounds 8 ounces. Suppose you are the woman's mail carrier and she asks you how much money will be saved by sending both gifts as one package instead of two. Make the necessary calculations to answer her question. (Hint: 16 ounces $=1$ pound.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 20

Juan wants to send a package weighing 6 pounds 1 ounce to a friend living in zone $2 .$ Standard postage would be $\$ 3.25 .$ How much could he save by sending the package standard postage instead of priority mail?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 21

List the top three most commonly owned pets in the United States.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 22

There are four types of pets that are owned in approximately equal numbers. What are they?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 23

Together, are there more pet dogs and cats than pet fish?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 24

How many more pet cats are there than pet dogs?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 25

For the years shown in the graph, has the production of zinc always exceeded the production of lead?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 26

Estimate how many times greater the amount of zinc produced in 2000 was compared to the amount of lead produced that year?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 27

What is the sum of the amounts of lead produced in $1990,2000,$ and $2007 ?$

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 28

For which metal, lead or zinc, has the production remained about the same over the years?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 29

In what years was the amount of zinc produced at least twice that of lead?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 30

Find the difference in the amount of zinc produced in 2007 and the amount produced in 2000

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 31

By how many metric tons did the amount of zinc produced increase between 1990 and $2007 ?$

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 32

Between which two years did the production of lead decrease?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 33

Which group (children, parents, or seniors) spent the most money on ice cream at Barney's Café?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 34

How much money did parents spend on ice cream?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 35

How much more money did seniors spend than parents?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 36

How much more money did seniors spend than children?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 37

Of the languages in the graph, which is spoken by the greatest number of people?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 38

Do more people speak Spanish or French?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 39

Together, do more people speak English, French, Spanish, Russian, and German combined than Chinese?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 40

Three pairs of languages shown in the graph are spoken by groups of the same size. Which pairs of languages are they?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 41

What percent of the world's population speak a language other than the eight shown in the graph?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 42

What percent of the world's population speak Russian or English?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 43

To the nearest one million, how many people in the world speak Chinese?
To the nearest one million, how many people in the world speak Chinese?

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 44

To the nearest one million, how many people in the world speak Arabic?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 45

How many U.S. ski resorts were in operation in $2004 ?$
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 46

How many U.S. ski resorts were in operation in $2008 ?$
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 47

Between which two years was there a decrease in the number of ski resorts in operation? (Hint: there is more than one answer.)
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 48

Between which two years was there an increase in the number of ski resorts in operation? (Hint: there is more than one answer.)
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 49

For which two years were the number of ski resorts in operation the same?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 50

Find the difference in the number of ski resorts in operation in 2001 and 2008
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 51

Between which two years was there the greatest decrease in the number of ski resorts in operation? What was the decrease?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 52

Between which two years was there the greatest increase in the number of ski resorts in operation? What was the increase?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 53

Which runner ran faster at the start of the race?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 54

At time $A$, which runner was ahead in the race?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 55

At what time during the race were the runners tied for the lead?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 56

Which runner stopped to rest first?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 57

Which runner dropped his watch and had to go back to get it?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 58

At which of these times $(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E})$ was runner 1 stopped and runner 2 running?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 59

Describe what was happening at time $E$. Who was running? Who was stopped?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 60

Which runner won the race?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 61

COMMUTING MILES An insurance company collected data on the number of miles its employees drive to and from work. The data are presented in the histogram below.
a. How many employees have a commute that is in the range of 15 to 19 miles per week?
b. How many employees commute 14 miles or less per week?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 62

NIGHT SHIFT STAFFING A hospital administrator surveyed the medical staff to determine the number of room calls during the night. She constructed the frequency polygon below.
a. On how many nights were there about 30 room calls?
b. On how many nights were there about 60 room calls?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 63

FILING A SINGLE RETURN Herb is single and has an adjusted income of $\$ 79,250 .$ Compute his federal income tax.
CAN'T COPY THE TABLE

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 64

FILING A JOINT RETURN Raul and his wife have a combined adjusted income of $\$ 57,100 .$ Compute their federal income tax if they file jointly.
CAN'T COPY THE TABLE

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 65

TAX-SAVING STRATEGY Angelina is single and has an adjusted income of $\$ 53,000$. If she gets married, she will gain other deductions that will reduce her income by $\$ 2,000,$ and she can file a joint return.
a. Compute her federal income tax if she remains single.
b. Compute her federal income tax if she gets married.
c. How much will she save in federal income tax by getting married?
CAN'T COPY THE TABLE

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 66

THE MARRIAGE PENALTY A single man with an adjusted income of $\$ 80,000$ is dating a single woman with an adjusted income of $\$ 75,000$.
a. Find the amount of federal income tax each person would pay on their adjusted income.
b. Add the results from part a.
c. If they get married and file a joint return, how much federal income tax will they have to pay on their combined adjusted incomes?
d. Would they have saved on their federal income taxes if they did not get married and paid as two single persons? Find the amount of the "marriage penalty."
CAN'T COPY THE TABLE

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 67

In which year was the largest percent of flights cancelled? Estimate the percent.
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 68

In which year was the smallest percent of flights cancelled? Estimate the percent.
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 69

Did the percent of cancelled flights increase or decrease between 2006 and $2007 ?$ By how much?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 70

Did the percent of cancelled flights increase or decrease between 2007 and $2008 ?$ By how much?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 71

How did the plane's altitude change between times $\mathrm{B}$ and C?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 72

At what time did the pilot first level off the airplane?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 73

When did the pilot first begin his descent to land the airplane?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 74

How did the plane's altitude change between times D and E?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 75

In which categories of moving violations have violations decreased since last month?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 76

Last month, which violation occurred most often?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 77

This month, which violation occurred least often?
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Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 78

Which violation has shown the greatest decrease in number since last month?
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Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 79

What were the average weekly earnings in mining for the year $1980 ?$
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 80

What were the average weekly earnings in construction for the year $1980 ?$
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 81

Were the average weekly earnings in mining and construction ever the same?
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Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 82

What was the difference in a miner's and a construction worker's weekly earnings in $1995 ?$
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 83

In the period between 2005 and 2008 , which occupation's weekly earnings were increasing more rapidly, the miner's or the construction worker's?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 84

Did the weekly earnings of a miner or a construction worker ever decrease over a five-year span?
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Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 85

In the period from 1980 to 2008 , which workers received the greatest increase in weekly earnings?
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Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 86

In what five-year span was the miner's increase in weekly earnings the smallest?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 87

What is the daily parking rate for Midtown New York?
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Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 88

What is the daily parking rate for Boston?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 89

How much more would it cost to park a car for five days in Boston compared to five days in San Francisco?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 90

How much more would it cost to park a car for five days in Midtown New York compared to five days in Boston?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 91

What percent of U.S. energy production comes from nuclear energy? Round to the nearest percent.
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 92

What percent of U.S. energy production comes from natural gas? Round to the nearest percent.
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Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 93

What percent of the total energy production comes from renewable and nuclear combined?
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Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 94

By what percent does energy produced from coal exceed that produced from crude oil?
CAN'T COPY THE GRAPH

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 95

NUMBER OF U.S. FARMS Use the data in the table below to make a bar graph showing the number of
U.S. farms for selected years from 1950 through 2007 .
$$\begin{array}{l|cc}\hline & \text { Number of } & \text { Average size } \\\text { U.S.farms } & \text { of U.S. farms } \\\text { Year } & \text { (in millions) } & \text { (acres) } \\\hline 1950 & 5.6 & 213 \\1960 & 4.0 & 297 \\1970 & 2.9 & 374 \\1980 & 2.4 & 426 \\1990 & 2.1 & 460 \\2000 & 2.2 & 436 \\2007 & 2.1 & 449
\end{array}$$

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 96

SIZE OF U.S. FARMS Use the data in the table below to make a line graph showing the average acreage of U.S. farms for selected years from 1950 through 2007 .
$$\begin{array}{l|cc}\hline & \text { Number of } & \text { Average size } \\\text { U.S.farms } & \text { of U.S. farms } \\\text { Year } & \text { (in millions) } & \text { (acres) } \\\hline 1950 & 5.6 & 213 \\1960 & 4.0 & 297 \\1970 & 2.9 & 374 \\1980 & 2.4 & 426 \\1990 & 2.1 & 460 \\2000 & 2.2 & 436 \\2007 & 2.1 & 449
\end{array}$$

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 97

COUPONS Each coupon value shown in the table below provides savings for shoppers. Make a line graph that relates the original price (in dollars, on the horizontal axis) to the sale price (in dollars, on the vertical axis).
CAN'T COPY THE TABLE

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Problem 98

DENTISTRY To study the effect of fluoride in preventing tooth decay, researchers counted the number of fillings in the teeth of 28 patients and recorded these results:
$3,7,11,21,16,22,18,8,12,3,7,2,8,19,12,19,12,10$
$13,10,14,15,14,14,9,10,12,13$
Tally the results by completing the table. Then make a histogram. The first bar extends from 0.5 to 5.5, the second bar from 5.5 to $10.5,$ and so on.
CAN'T COPY THE TABLE

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Problem 99

What kind of presentation (table, bar graph, line graph, circle graph, pictograph, or histogram) is most appropriate for displaying each type of information? Explain your choices.
$\cdot$ The percent of students at a college, classified by major
$\cdot$ The percent of biology majors at a college each year since 1970
$\cdot$ The number of hours a group of students spent studying for final exams
$\cdot$ The ethnic populations of the ten largest cities The average annual salary of corporate executives for ten major industries

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Problem 100

Explain why a histogram is a special type of bar graph.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 101

Write the prime numbers between 10 and 30 .

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 102

Write the first ten composite numbers.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 103

Write the even whole numbers less than 6 that are not prime.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator

Problem 104

Write the odd whole numbers less than 20 that are not prime.

Kerry Thornton-Genova

Kerry Thornton-Genova

Numerade Educator