Fundamentals of Statistics

Michael Sullivan III

Chapter 2 Organizing and Summarizing Data - all with Video Answers

Educators

Section 1

Organizing Qualitative Data

01:11

Problem 1

Define raw data in your own words.

Tyler Moulton

Numerade Educator

01:03

Problem 2

A frequency distribution lists the __________ of occurrences of each category of data, while a relative frequency distribution lists the __________ of occurrences of each category of data.

Tyler Moulton

Numerade Educator

01:09

Problem 3

When constructing a frequency distribution, why is it a good idea to add up the frequencies?

Tyler Moulton

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01:11

Problem 4

In a relative frequency distribution, what should the relative frequencies add up to?

Tyler Moulton

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01:06

Problem 5

What is a Pareto chart?

Tyler Moulton

Numerade Educator

01:17

Problem 6

Why should relative frequencies be used when comparing two data sets?

Tyler Moulton

Numerade Educator

01:11

Problem 7

Explain why Pareto charts might be preferred over bar graphs.

Tyler Moulton

Numerade Educator

01:24

Consider the information in the "Why we can't lose weight" chart shown below which is in the USA Today style of graph. Could the information provided be organized into a pie chart? Why or why not?
(GRAPH CAN'T COPY)

Tyler Moulton

Numerade Educator

01:10

Problem 9

The pie chart at the right, the type we see in USA Today, depicts the bucket size golfers choose while at the driving range.
(a) What is the most popular size? What percentage of golfers choose this size?
(b) What is the least popular size? What percentage of golfers choose this size?
(c) What percentage of golfers choose a medium-sized bucket?
(GRAPH CAN'T COPY)

Tyler Moulton

Numerade Educator

03:40

Problem 10

The USA Today-type chart shows the most frequent cosmetic surgeries for women in 2003
(a) If women had 1,548,000 cosmetic surgeries in 2003 how many of them were for liposuction?
(b) How many were for eyelid surgery?
(c) What percentage of surgeries are not accounted for in the graph?
(GRAPH CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

01:06

Problem 11

The following Pareto chart represents the top 10 countries in Internet users as of February 2005
(a) Which country has the most Internet users?
(b) Approximately what is the Internet usage in Canada?
(c) Approximately how many more users are in China than in Japan?
(GRAPH CAN'T COPY)

Tyler Moulton

Numerade Educator

04:04

Problem 12

Every year the U.S. Census Bureau counts the number of people living in poverty. The bureau uses money income thresholds as its definition of poverty, so noncash benefits such as Medicaid and food stamps do not count toward poverty thresholds. For example, in 2002 the poverty threshold for a family of three was $\$ 14,348 .$ The bar chart represents the number of people living in poverty in the United States in $2003,$ by ethnicity, based on March 2004 estimates.
(GRAPH CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

05:01

Problem 13

The following bar chart represents the number of voters who cast votes for the top five vote-getters and all others in the 2004 presidential election. The number of votes received for each candidate appears above the bar.
(a) How many votes were cast for Michael Badnarik of the Libertarian Party?
(b) What percent of the votes was cast for George W. Bush? For John F. Kerry?
(c) To receive presidential election funds, a candidate must garner at least $5 \%$ of the vote. Will Ralph Nader receive presidential election funds?
(GRAPH CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

02:20

Problem 14

In a study conducted by the Better Business Bureau and Javelin Strategy and Research, victims of identity fraud were asked, "Who was the person who misused your personal information?" The following Pareto chart represents the results for cases in the year 2004 for which the perpetrator's identity was known.
(a) Approximately what percentage of identity-fraud victims were victimized by a family member or relative?
(b) If there were 9.3 million identity-fraud victims in 2004 , how many were victimized by someone at a company with access to personal information?
(GRAPH CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

07:28

Problem 15

The following side-by-side bar graph represents the proportion of households using four common sources of home heating fuel for the years $1978,1987,1997,$ and 2001
(a) What proportion of households used electricity as their main source of home heating fuel in $1978 ?$ in $1997 ?$
(b) What was the most popular source of home heating fuel in $1987 ?$
(c) If there were 107 million U.S. households in 2001 , how many used LPG as their main source of home heating fuel?
(d) What might account for the rise in homes that use electricity as the main source of home heating fuel?
(e) Which source of home heating fuel has been decreasing rather steadily? What might account for this?
(f) Which sources of home heating fuel have remained rather steady?
(GRAPH CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

04:53

Problem 16

The following side-by-side bar graph represents the number of doctorate recipients from U.S. universities within broad fields of study for the years $1983,1993,$ and 2003
(a) How many more engineering doctorates were awarded in 1993 than in $2003 ?$
(b) In $2003,$ what percentage of doctoral recipients received degrees in physical science? in education?
(c) What field of study consistently decreased in the number of doctoral degree recipients in the 3 years of the survey?
(d) Which field of study had the largest increase in the number of doctoral degree recipients in the 3 years of the survey?
(GRAPH CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

04:20

Problem 17

For fiscal year 2003 (October 1 , 2002 to September 30,2003 ), the federal government's income was $\$ 1,782.3$ billion. The various sources of income are broken down in the following table.
(a) Construct a relative frequency distribution of the data shown.
(b) What percentage of total income is attributable to individual income taxes?
(c) Construct a frequency bar graph of the data.
(d) Construct a relative frequency bar graph of the data.
(e) Construct a pie chart of the data.
(f) In your opinion, which graph appears to place more emphasis on social insurance taxes as a source of income, the relative frequency bar graph or the pie chart? Why?
(TABLE CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

06:55

Problem 18

Government Expenditures For fiscal year 2003 (October
1,2002 to September 30,2003 ), the federal government spent $\$ 2,158$ billion. The breakdown of expenditures is given in the following table.
(a) Construct a relative frequency distribution of the data shown.
(b) What percentage of total expenditures is attributable to net interest on debt?
(c) Construct a frequency bar graph of government expenditures.
(d) Construct a relative frequency bar graph of government expenditures.
(e) Construct a pie chart of government expenditures.
(f) In your opinion, which graph appears to place more emphasis on net interest on the debt, the relative frequency bar graph or the pie chart? Why?
(TABLE CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

06:10

Problem 19

In a national survey conducted by the Centers for Disease Control to determine health-risk behaviors among college students, college students were asked, "How often do you wear a seat belt when riding in a car driven by someone else?" The frequencies were as follows:
(a) Construct a relative frequency distribution.
(b) What percentage of respondents answered "Always"?
(c) What percentage of respondents answered "Never" or "Rarely"?
(d) Construct a frequency bar graph.
(e) Construct a relative frequency bar graph.
(f) Construct a pie chart.
(g) Suppose that a representative from the Centers for Disease Control says, "52.7\% of all college students never wear a seat belt." Is this a descriptive or inferential statement?
(TABLE CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

11:36

Problem 20

College Survey In a national survey conducted by the Centers for Disease Control to determine health-risk behaviors among college students, college students were asked, "How often do you wear a seat belt when driving a car?" The frequencies were as follows:
(a) Construct a relative frequency distribution.
(b) What percentage of respondents answered "Always"?
(c) What percentage of respondents answered "Never" or "Rarely"?
(d) Construct a frequency bar graph.
(e) Construct a relative frequency bar graph.
(f) Construct a pie chart.
(g) Compute the relative frequencies of "Never," compute the rela "Rarely," "Sometimes," "Most of the time," and "Always," excluding those that do not drive. Compare with those in Problem 19. What might you conclude?
(h) Suppose that a representative from the Centers for Disease Control says, "$2.5\%$" of the college students in this survey responded that they never wear a seat belt." Is this a descriptive or inferential statement?
(TABLE CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

04:36

Problem 21

The following data represent the region of birth of foreign-born residents of the United States in 2003
(a) Construct a relative frequency distribution.
(b) What percentage of foreign-born residents was born in Asia?
(c) Construct a frequency bar graph.
(d) Construct a relative frequency bar graph.
(e) Construct a pie chart.
(TABLE CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

03:47

Problem 22

Robbery The following data represent the number of offenses for various robberies in 2003
(a) Construct a relative frequency distribution.
(b) What percentage of robberies was of gas stations?
(c) Construct a frequency bar graph.
(d) Construct a relative frequency bar graph.
(e) Construct a pie chart.
(TABLE CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

05:37

Problem 23

On the basis of the 2003 Current Population Survey, there were 88.7 million males and 96.6 million females 25 years old or older in the United States. The educational attainment of the males and females was as follows:
(a) Construct a relative frequency distribution for males.
(b) Construct a relative frequency distribution for females.
(c) Construct a side-by-side relative frequency bar graph.
(d) Compare each gender's educational attainment. Make
a conjecture about the reasons for the differences.
(TABLE CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

05:26

Problem 24

The following data represent the number of people who had Internet access in the years 2000 and 2003 by level of education. Data are in thousands of U.S. residents.
(a) Construct a relative frequency distribution for 2000 .
(b) Construct a relative frequency distribution for 2003
(c) Construct a side-by-side relative frequency bar graph.
(d) Compare each year's Internet access. Make some conjectures about the reasons for any differences or similarities
(TABLE CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

06:34

Problem 25

A criminologist wanted to know if there was any relation between age and gender of murder victims. The following data represent the number of male and female murder victims by age in 2002
(a) Construct a relative frequency distribution for males.
(b) Construct a relative frequency distribution for females.
(c) Construct a side-by-side relative frequency bar graph.
(d) Compare each gender's age percentages. Make a conjecture about the reasons for the differences or similarities.
(TABLE CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

04:30

Problem 26

DuPont Automotive is a major supplier of paint to the automotive industry. It conducted a survey of 100 randomly selected autos in the luxury car segment and 100 randomly selected autos in the sports car segment that were recently purchased and obtained the following colors.
(a) Construct a relative frequency distribution for each car type.
(b) Draw a side-by-side relative frequency bar graph.
(c) Compare the colors for the two types of car. Make a conjecture about the reasons for the differences.
(TABLE CAN'T COPY)

Jeremiah Mbaria

Numerade Educator

09:17

Problem 27

An exit poll was conducted in Los Alamos County, New Mexico, in which a random sample of 40 voters revealed whom they voted for in the presidential election. The results of the survey are as follows:
$$\begin{array}{llll}
\text { Kerry } & \text { Kerry } & \text { Bush } & \text { Bush } \\
\hline \text { Bush } & \text { Kerry } & \text { Kerry } & \text { Bush } \\
\hline \text { Kerry } & \text { Bush } & \text { Kerry } & \text { Bush } \\
\hline \text { Bush } & \text { Bush } & \text { Kerry } & \text { Kerry } \\
\hline \text { Kerry } & \text { Bush } & \text { Bush } & \text { Kerry } \\
\hline \text { Badnarik } & \text { Bush } & \text { Kerry } & \text { Bush } \\
\hline \text { Kerry } & \text { Bush } & \text { Kerry } & \text { Bush } \\
\hline \text { Bush } & \text { Bush } & \text { Kerry } & \text { Kerry } \\
\hline \text { Bush } & \text { Bush } & \text { Bush } & \text { Nader } \\
\hline \text { Bush } & \text { Kerry } & \text { Bush } & \text { Kerry }
\end{array}$$
(a) Construct a frequency distribution.
(b) Construct a relative frequency distribution.
(c) Construct a frequency bar graph.
(d) Construct a relative frequency bar graph.
(e) Construct a pie chart.
(f) On the basis of the data, make a conjecture about which candidate will win Los Alamos County. Would your conjecture be descriptive statistics or inferential statistics? If George W. Bush wins Los Alamos County, what conclusions might be drawn, assuming that the sample was conducted appropriately? Would you be confident in making this prediction with a sample of $40 ?$ If the sample consisted of 100 voters, would your confidence increase? Why?

Jeremiah Mbaria

Numerade Educator

06:55

Problem 28

The following data represent the diagnoses of a random sample of 20 patients admitted to a hospital.
$$\begin{array}{lll}
\text { Cancer } & \begin{array}{l}
\text { Motor vehicle } \\
\text { accident }
\end{array} & \begin{array}{l}
\text { Congestive heart } \\
\text { failure }
\end{array} \\
\hline \text { Gunshot wound } & \text { Fall } & \text { Gunshot wound } \\
\hline \text { Gunshot wound } & \begin{array}{l}
\text { Motor vehicle } \\
\text { accident }
\end{array} & \text { Gunshot wound } \\
\hline \text { Assault } & \begin{array}{l}
\text { Motor vehicle } \\
\text { accident }
\end{array} & \text { Gunshot wound } \\
\hline \begin{array}{l}
\text { Motor vehicle } \\
\text { accident }
\end{array} & \begin{array}{l}
\text { Motor vehicle } \\
\text { accident }
\end{array} & \text { Gunshot wound } \\
\hline \begin{array}{l}
\text { Motor vehicle } \\
\text { accident }
\end{array} & \text { Gunshot wound } & \begin{array}{l}
\text { Motor vehicle } \\
\text { accident }
\end{array} \\
\hline \text { Fall } & \text { Gunshot wound } \\
\hline \text { Source Tamela Ohm, student at Joliet Junior College }
\end{array}$$
(a) Construct a frequency distribution.
(b) Construct a relative frequency distribution.
(c) Which diagnosis had the most admissions?
(d) What percentage of diagnoses was motor vehicle accidents?
(e) Construct a frequency bar graph.
(f) Construct a relative frequency bar graph.
(g) Construct a pie chart.
(h) Suppose that an admission specialist at the hospital stated that $40 \%$ of all admissions were gunshot wounds. Would this statement be descriptive or inferential? Why?

Jeremiah Mbaria

Numerade Educator

06:24

Problem 29

You are a prospective baseball agent and are in search of clients. You would like to recruit the highest-paid players as clients, so you perform a study in which you identify the 24 top-paid players for the 2004 season and their positions. The table shows the results of your study.
\begin{array}{ll}
\hline \text { Player } & \text { Position } \\
\hline \text { Manny Ramirez } & \text { Left field } \\
\hline \text { Alex Rodriquez } & \text { Third base } \\
\hline \text { Carlos Delgado } & \text { First base } \\
\hline \text { Derek Jeter } & \text { Shortstop } \\
\hline \text { Barry Bonds } & \text { Left field } \\
\hline \text { Pedro Martinez } & \text { Pitcher } \\
\hline \text { Mo Vaughn } & \text { First base } \\
\hline \text { Shawn Green } & \text { Right field } \\
\hline \text { Mike Piazza } & \text { Catcher } \\
\hline \text { Jeff Bagwell } & \text { First base } \\
\hline \text { Randy Johnson } & \text { Pitcher } \\
\hline \text { Mike Mussina } & \text { Pitcher } \\
\hline \text { Sammy Sosa } & \text { Right field } \\
\hline \text { Kevin Brown } & \text { Pitcher } \\
\hline \text { Chipper Jones } & \text { Third base } \\
\hline \text { Mike Hampton } & \text { Pitcher } \\
\hline \text { Magglio Ordonez } & \text { Right field } \\
\hline \text { Chan Ho Park } & \text { Pitcher } \\
\hline \text { Gary Sheffield } & \text { Right field } \\
\hline \text { Larry Walker } & \text { Right field } \\
\hline \text { Ken Griffey,Jr. } & \text { Center field } \\
\hline \text { Richard Hidalgo } & \text { Right field } \\
\hline \text { Andruw Jones } & \text { Center field } \\
\hline \text { Matt Morris } & \text { Pitcher } \\
\hline \text { Source: usatodaycom } &
\end{array}
(a) Construct a frequency distribution of position.
(b) Construct a relative frequency distribution of position.
(c) Which position appears to be the most lucrative? For which position would you recruit?
(d) Are there any positions that you would avoid recruiting? Why?
(e) Draw a frequency bar graph.
(f) Draw a relative frequency bar graph.
(g) Draw a pie chart.

Jeremiah Mbaria

Numerade Educator

08:13

Problem 30

A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown:
$$\begin{array}{lllll}
\hline O & O & A & A & O \\
\hline B & O & B & A & O \\
\hline A B & B & A & B & A B \\
\hline O & O & A & A & O \\
\hline A B & O & A & B & A \\
\hline O & A & A & O & A \\
\hline O & A & O & A B & A \\
\hline O & B & A & A & O \\
\hline O & O & O & A & O \\
\hline O & A & O & A & O
\end{array}$$
(a) Construct a frequency distribution.
(b) Construct a relative frequency distribution.
(c) According to the data, which blood type is most common?
(d) According to the data, which blood type is least common?
(e) Use the results of the sample to conjecture the percentage of the population that has type O blood. Is this an example of descriptive or inferential statistics?
(f) Contact a local hospital and ask them the percentage of the population that is blood type O. Why might the results differ?
(g) Draw a frequency bar graph.
(h) Draw a relative frequency bar graph.
(i) Draw a pie chart.

Jeremiah Mbaria

Numerade Educator

05:41

Problem 31

According to the Modern Language Association, the number of college students studying foreign language is increasing. The following data represent the foreign language being studied based on a simple random sample of 30 students learning a foreign language.
$$\begin{array}{lllll}
\hline \text { Spanish } & \text { Chinese } & \text { Spanish } & \text { Spanish } & \text { Spanish } \\
\hline \text { Chinese } & \text { German } & \text { Spanish } & \text { Spanish } & \text { French } \\
\hline \text { Spanish } & \text { Spanish } & \text { Japanese } & \text { Latin } & \text { Spanish } \\
\hline \text { German } & \text { German } & \text { Spanish } & \text { Italian } & \text { Spanish } \\
\hline \text { Italian } & \text { Japanese } & \text { Chinese } & \text { Spanish } & \text { French } \\
\hline \text { Spanish } & \text { Spanish } & \text { Russian } & \text { Latin } & \text { French } \\
\hline
\end{array}$$
(a) Construct a frequency distribution.
(b) Construct a relative frequency distribution.
(c) Construct a frequency bar graph.
(d) Construct a relative frequency bar graph.
(e) Construct a pie chart.

Jeremiah Mbaria

Numerade Educator

04:49

Problem 32

The following table lists the presidents of the United States and their state of birth.
$$\begin{array}{ll|lllll}
\hline \text { President } & \text { State of Birth } & \text { President } & \text { State of Birth } & \text { President } & \text { State of Birth } \\
\hline \text { Washington } & \text { Virginia } & \text { Lincoln } & \text { Kentucky } & \text { Coolidge } & \text { Vermont } \\
\hline \text { LAdams } & \text { Massachusetts } & \text { A.Johnson } & \text { North Carolina } & \text { Hoover } & \text { Iowa } \\
\hline \text { Jefferson } & \text { Virginia } & \text { Grant } & \text { Ohio } & \text { F.D. Roosevelt } & \text { New York } \\
\hline \text { Madison } & \text { Virginia } & \text { Hayes } & \text { Ohio } & \text { Truman } & \text { Missouri } \\
\hline \text { Monroe } & \text { Virginia } & \text { Garfield } & \text { Ohio } & \text { Eisenhower } & \text { Texas } \\
\hline \text { L O.Adams } & \text { Massachusetts } & \text { Arthur } & \text { Vermont } & \text { Kennedy } & \text { Massachusetts } \\
\hline \text { Jackson } & \text { South Carolina } & \text { Qeveland } & \text { New Jersey } & \text { L. B.Johnson } & \text { Texas } \\
\hline \text { Van Buren } & \text { New York } & \text { B. Harrison } & \text { Ohio } & \text { Nixon } & \text { California } \\
\hline \text { W.H.Harrison } & \text { Virginia } & \text { Cleveland } & \text { New Jersey } & \text { Ford } & \text { Nebraska } \\
\hline \text { Tyler } & \text { Virginia } & \text { McKinley } & \text { Ohio } & \text { Carter } & \text { Georgia } \\
\hline \text { Polk } & \text { North Carolina } & \text { T. Roosevelt } & \text { New York } & \text { Reagan } & \text { Illinois } \\
\hline \text { Taylor } & \text { Virginia } & \text { Taft } & \text { Ohio } & \text { George H. Bush } & \text { Massachusetts } \\
\hline \text { Fillmore } & \text { New York } & \text { Wilson } & \text { Virginia } & \text { Cinton } & \text { Arkansas } \\
\hline \text { Pierce } & \text { New Hampshire } & \text { Harding } & \text { Ohio } & \text { George W.Bush } & \text { Connecticut } \\
\hline \text { Buchanan } & \text { Pennsylvania } & & &
\end{array}$$
(a) Construct a frequency bar graph for state of birth.
(b) Which state has yielded the most presidents?
(c) Explain why the answer obtained in part (b) may be considered to be misleading.

Jeremiah Mbaria

Numerade Educator

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