Question 1

A real estate company kept a database on the apartments in a certain city.The percentages of various types of apartments are listed below. $$\begin{array} { l | c } 
\text { Type } & \text { Percent } \
\hline \text { Studio } & 15.9 \
\hline \text { 1-bedroom } & 25.5 \
\hline \text { 2-bedroom } & 45.8 \
\hline \text { 3-bedroom } & 10.1
\end{array}$$ What percentage of the apartments in the city are 1-bedroom or 2-bedroom apartments?

Accepted Answer

C

Question 2

A newspaper surveyed its subscribers as to which section of the paper they read first.The results are listed below. $$\begin{array} { l | c } 
\text { Section } & \text { Percent } \
\hline \text { Front page } & 18.3 \
\hline \text { Sports } & 25.2 \
\hline \text { Business } & 13.9 \
\hline \text { Comics } & 22.1 \
\hline \text { Horoscope } & 13.7
\end{array}$$ Is it reasonable to conclude that 39.1% of the paper's subscribers read the business or sports sections first?

Accepted Answer

The categories "Business" and "Sports" do not overlap, meaning a subscriber who reads the business section first is distinct from one who reads the sports section first. Therefore, their percentages can be added to determine the total percentage of subscribers who read either section first.

Question 3

The City of Windsor Department of Parks and Recreation is planning to build a recreation centre in one of the city's parks.They conducted a poll to find out the types of physical activities the local population would be interested in.The poll was based on telephone responses from 1013 randomly selected adults.The table shows the percentages of people who expressed interest in various activities. $$\begin{array} { l | c } 
{ \text { Activity } } & \text { Percent } \
\hline \text { Running/Walking } & 56 \
\text { Weight Training } & 45 \
\text { Biking } & 34 \
\text { Aerobics } & 25 \
\text { Swimming } & 16
\end{array}$$ Is it reasonable to conclude that 59% expressed interest in either biking or aerobics?

Accepted Answer

The categories of biking and aerobics could overlap, meaning some individuals might be interested in both activities. Therefore, adding the percentages directly without accounting for potential overlap could lead to an inaccurate conclusion.

Question 4

The City of Windsor Department of Parks and Recreation is planning to build a recreation centre in one of the city's parks.They conducted a poll to find out which of five types of physical activities the local population would be interested in.The poll was based on telephone responses from 1013 randomly selected adults.The table shows the percentages of people who expressed interest in various activities. $$\begin{array} { l | c } 
{ \text { Activity } } & \text { Percent } \
\hline \text { Running/Walking } & 56 \% \
\text { Weight Training } & 48 \% \
\text { Biking } & 33 \% \
\text { Aerobics } & 25 \% \
\text { Swimming } & 13 \%
\end{array}$$ Which of the following displays is/are appropriate to describe the data for these five activities? (More than one display may be appropriate.) 
I  
II  
III

Accepted Answer

The most appropriate display to represent this data is a stacked bar graph, where each bar represents the total percentage of people interested in each activity, and the different colors within each bar represent the percentage of people interested in each age group. Option I displays this information accurately and in a visually clear manner. Option II displays the data in a stacked bar graph, as well as a pie chart, which is unnecessary and can make it more challenging to compare the different activities. Option III shows a scatter plot, which is not appropriate for this type of data. Therefore, the best choice is A) I.

Question 5

Of the 1606 applicants to a college program,456 were Black or Hispanic,300 were Asian,and 850 were White.Summarize the relative frequency distribution of ethnicity with a sentence or two in the proper context.

Accepted Answer

To calculate the relative frequency, divide the number of students of each ethnicity by the total number of applicants and multiply by 100 to get a percentage. For Black or Hispanic, $ \frac{456}{1606} \times 100 \approx 28\% $; for Asian, $ \frac{300}{1606} \times 100 \approx 19\% $; for White, $ \frac{850}{1606} \times 100 \approx 53\% $.

Question 6

Statistics Canada gives the following mortality data for Canada in 2011. $$\begin{array} { l | c } 
{ \text { Cause of Death } } & \text { Percent } \
\hline \text { Cancer } & 29.9 \
\text { Heart disease } & 19.7 \
\text { Stroke } & 5.5 \
\text { Respiratory diseases } & 4.6 \
\text { Accidents } & 4.4
\end{array}$$ Is it reasonable to conclude that cancer or accidents were the cause of approximately 34.3% of deaths in 2011?

Accepted Answer

Cancer and accidents are separate categories, and therefore their percentages do not overlap. It is reasonable to conclude that the sum of their percentages represents the proportion of deaths due to these causes, which is 34.3%. The fact that the percentages do not add up to 100% is not relevant to this conclusion. Option C is also correct, but option B is more precise in explaining why it is reasonable to add the percentages of cancer and accidents. Options A, D, and E are incorrect.

Question 7

The Centers for Disease Control in the U.S.A.lists causes of death for individual states in 2002.The mortality data for the five leading causes of death for one state is given. $$\begin{array} { l | c } 
{ \text { Cause of Death } } & \text { Percent } \
\hline \text { Heart Disease } & 28.5 \% \
\text { Cancer } & 23.2 \% \
\text { Circulatory diseases and stroke } & 7.5 \% \
\text { Respiratory diseases } & 5.5 \% \
\text { Accidents } & 4.8 \%
\end{array}$$ Which of the following displays is/are appropriate to describe the data for all causes of death? (More than one display may be appropriate.) 
I   
II
 
III

Accepted Answer

The answer of The Centers for Disease Control in the...

Question 8

The City of Windsor Department of Parks and Recreation is planning to build a recreation centre in one of the city's parks.They conducted a poll to find out which of five types of physical activities the local population would be interested in.The poll was based on telephone responses from 1013 randomly selected adults.The table shows the percentages of people who expressed interest in various activities. $$\begin{array} { l | c } 
{ \text { Activity } } & \text { Percent } \
\hline \text { Running/Walking } & 56 \% \
\text { Weight Training } & 48 \% \
\text { Biking } & 33 \% \
\text { Aerobics } & 25 \% \
\text { Swimming } & 13 \%
\end{array}$$ Which of the following displays is/are appropriate to describe the data for these five activities? (More than one display may be appropriate.)

Accepted Answer

The answer of The City of Windsor Department of Parks...

Question 9

A poll asked adults which activities they had engaged in during the past month.The results are listed below. $$\begin{array} { l | c } 
\text { Activity } & \text { Percent } \
\hline \text { Dinner out } & 55.7 \
\hline \text { Sporting event } & 15.9 \
\hline \text { Movie } & 45.6 \
\hline \text { Stroll } & 5.1
\end{array}$$ Is it reasonable to conclude that 61.5% of those polled had seen a movie or gone to a sporting event during the past month?

Accepted Answer

The categories "seen a movie" and "gone to a sporting event" overlap, as it is possible for individuals to have done both. Therefore, simply adding the percentages of these categories would result in double-counting some individuals and an overestimation of the total percentage.

Question 10

The City of Windsor Department of Parks and Recreation is planning to build a recreation centre in one of the city's parks.They conducted a poll to find out which of five types of physical activities the local population would be interested in.The poll was based on telephone responses from 1013 randomly selected adults.The table shows the percentages of people who expressed interest in various activities. $$\begin{array} { l | c } 
{ \text { Activity } } & \text { Percent } \
\hline \text { Running/Walking } & 56 \% \
\text { Weight Training } & 48 \% \
\text { Biking } & 33 \% \
\text { Aerobics } & 25 \% \
\text { Swimming } & 13 \%
\end{array}$$ Which of the following displays is/are appropriate to describe the data for these five activities? (More than one display may be appropriate.) 
I  
II  
III

Accepted Answer

The answer of The City of Windsor Department of Parks...

Question 11

The City of Windsor Department of Parks and Recreation is planning to build a recreation centre in one of the city's parks.They conducted a poll to find out the types of physical activities the local population would be interested in.The poll was based on telephone responses from 1013 randomly selected adults.The table shows the percentages of people who expressed interest in various activities. $$\begin{array} { l | c } 
{ \text { Activity } } & \text { Percent } \
\hline \text { Running/Walking } & 58 \
\text { Weight Training } & 50 \
\text { Biking } & 34 \
\text { Aerobics } & 24 \
\text { Swimming } & 13
\end{array}$$ What percent of adults polled did not express interest in any of these activities?

Accepted Answer

The percentages could overlap because individuals might be interested in more than one activity, making it impossible to determine the percentage of adults not interested in any activity without specific data on unique preferences.

Question 12

The Centers for Disease Control in the U.S.A.lists causes of death for individual states in 2002.The mortality data for the five leading causes of death for one state is given. $$\begin{array} { l | c } 
{ \text { Cause of Death } } & \text { Percent } \
\hline \text { Heart Disease } & 28.5 \% \
\text { Cancer } & 23.2 \% \
\text { Circulatory diseases and stroke } & 7.5 \% \
\text { Respiratory diseases } & 5.5 \% \
\text { Accidents } & 4.8 \%
\end{array}$$ Which of the following displays is/are appropriate to describe the data for all causes of death? (More than one display may be appropriate.)   
I  
II  
III

Accepted Answer

Both II and III are appropriate displays for describing mortality data for all causes of death. II is a horizontal bar chart, which is effective in comparing the number of deaths for each cause. III is a stacked bar chart, which can show the total number of deaths for each sex and age group, as well as the contribution of each cause to the total number of deaths. I is not appropriate as a display for the data for all causes of death because it only shows the leading causes of death, which may not include less common but still significant causes. Therefore, the correct answer is C - II and III.

Question 13

A newspaper surveyed its subscribers as to which section of the paper they read first.The results are listed below. $$\begin{array} { l | c } 
\text { Section } & \text { Percent } \
\hline \text { Front page } & 18.3 \
\hline \text { Sports } & 25.2 \
\hline \text { Business } & 13.9 \
\hline \text { Comics } & 22.1 \
\hline \text { Horoscope } & 13.7
\end{array}$$ What percent of subscribers read a section of the paper not listed above first?

Accepted Answer

To find the percent of subscribers who read a section not listed, add the given percentages and subtract from 100%. $18.3 + 25.2 + 13.9 + 22.1 + 13.7 = 93.2$. $100 - 93.2 = 6.8\%$.

Question 14

The Centers for Disease Control in the U.S.A.lists causes of death for individual states in 2002.The mortality data for the five leading causes of death for one state is given. $$\begin{array} { l | c } 
{ \text { Cause of Death } } & \text { Percent } \
\hline \text { Heart Disease } & 28.5 \% \
\text { Cancer } & 23.2 \% \
\text { Circulatory diseases and stroke } & 7.5 \% \
\text { Respiratory diseases } & 5.5 \% \
\text { Accidents } & 4.8 \%
\end{array}$$ Which of the following displays is/are appropriate to describe the data for all causes of death? (More than one display may be appropriate.) 
I  
II 
 
III

Accepted Answer

The answer of The Centers for Disease Control in the...

Question 15

Statistics Canada gives the following mortality data for Canada in 2011. $$\begin{array} { l | c } 
{ \text { Cause of Death } } & \text { Percent } \
\hline \text { Cancer } & 29.9 \
\text { Heart disease } & 19.7 \
\text { Stroke } & 5.5 \
\text { Respiratory diseases } & 4.6 \
\text { Accidents } & 4.4
\end{array}$$ What percent of deaths were from causes not listed here?

Accepted Answer

To find the percent of deaths from causes not listed, add the given percentages and subtract from 100%. $29.9 + 19.7 + 5.5 + 4.6 + 4.4 = 64.1%$. Subtracting this from 100% gives $100 - 64.1 = 35.9%$.

Question 16

The focus of a recent survey was on teenagers' familiarity with and use of modern technology.The teenagers were asked if they used each of the following technologies on a daily basis and if the technology was critically important to own.For each question,the percentage of those responding "Yes" is given.Subtracting the "Use daily" percentage from the "Critically important to own" percentage gives the "Importance Gap".Here are the results: $$\begin{array} { | l | c | c | c | } 
\hline & \begin{array} { c } 
\text { Use } \
\text { daily }
\end{array} & \begin{array} { c } 
\text { Critically } \
\text { important } \
\text { to own }
\end{array} & \begin{array} { c } 
\text { Importance } \
\text { gap }
\end{array} \
\hline \text { Computer } & 46 \% & 78 \% & 32 \
\text { Telephone } & 52 \% & 69 \% & 17 \
\text { DVD } & 39 \% & 52 \% & 13 \
\text { Calculator } & 71 \% & 77 \% & 6 \
\text { Stereo/audio } & 90 \% & 72 \% & - 18 \
\text { Video games } & 48 \% & 21 \% & - 27 \
\hline
\end{array}$$ Which of the following displays is the most appropriate for these data?
 I  
II  
III

Accepted Answer

The answer of The focus of a recent survey was...

Question 17

A prediction of the number of medals to be won by various countries in the 2014 Winter Olympics was made using past Olympics data.The predicted values are listed in the table below. $$\begin{array} { l | c } 
\text { Country } & \text { Medals } \
\hline \text { Germany } & 37 \
\text { USA } & 36 \
\text { Norway } & 27 \
\text { Canada } & 24 \
\text { Austria } & 16 \
\text { Russia } & 16 \
\text { Italy } & 15 \
\text { France } & 15 \
\text { Switzerland } & 13 \
\text { China } & 10
\end{array}$$ $$\begin{array} { l | c } 
\text { Country } & \text { Medals } \
\hline \text { Netherlands } & 5 \
\text { Finland } & 4 \
\text { Sweden } & 4 \
\text { Korea } & 3 \
\text { Bulgaria } & 3 \
\text { Great Britain } & 2 \
\text { Australia } & 2 \
\text { Japan } & 2 \
\text { Poland } & 1 \
\text { Spain } & 1
\end{array}$$ Which of the following displays is the most appropriate for these data? 
I 
 II  
III

Accepted Answer

The most appropriate display for these data is a horizontal bar graph which is shown in display II. This is because the predicted values are categorical (countries) and the data is numerical (number of medals), making a bar graph the most appropriate choice. Display I is inappropriate because it shows data points on a two-dimensional scatterplot, which is not appropriate for this type of data. Display III is also inappropriate because it is a line graph, which is not appropriate for categorical data.

Question 18

The Centers for Disease Control in the U.S.A.lists causes of death for individual states in 2002.The mortality data for the five leading causes of death for one state is given. $$\begin{array} { l | c } 
{ \text { Cause of Death } } & \text { Percent } \
\hline \text { Heart Disease } & 28.5 \% \
\text { Cancer } & 23.2 \% \
\text { Circulatory diseases and stroke } & 7.5 \% \
\text { Respiratory diseases } & 5.5 \% \
\text { Accidents } & 4.8 \%
\end{array}$$ Which of the following displays is/are appropriate to describe the data for all causes of death? (More than one display may be appropriate.) 
I  
II 
 
III

Accepted Answer

The answer of The Centers for Disease Control in the...

Question 19

Students in a Political Science course were asked to describe their politics as "Liberal","Moderate",or "Conservative." Here are the results: $\begin{array}{l}
Sex
\begin{array}{l}
\begin{array} { | l | c c c | c | } 
&&\text { Politics }\\
\hline & \text { Liberal } & \text { Moderate } & \text { Conservative } & \text { Total } \
\hline \text { Female } & 45 & 49 & 12 & 106 \
\text { Male } & 64 & 53 & 25 & 142 \
\hline \text { Total } & 109 & 102 & 37 & 248 \
\hline
\end{array}
\end{array}
\end{array}$ Which graphical display shows the marginal distribution of politics in the class? 
I  
II  
III

Accepted Answer

The bar graph in option C shows the marginal distribution of politics in the class. The x-axis displays the three categories - Liberal, Moderate, and Conservative, and the y-axis displays the frequency or count of students in each category. Therefore, this graph represents the marginal distribution of politics in the class. Option A and Option B do not show the marginal distribution of politics and Option D includes all the graphs, which is not necessary as we only need one graph to display the marginal distribution.

Question 20

Of the 1470 applicants to a college program,760 were accepted,269 were wait-listed,and 441 were turned away for lack of space.Find the relative frequency distribution of the decisions made,and write a sentence describing it.

Accepted Answer

To find the relative frequency distribution, divide the number of students in each category by the total number of applicants. Accepted: 760/1470 = 51.7% (approximately 52%), Wait-listed: 269/1470 = 18.3% (approximately 18%), Turned away: 441/1470 = 30%. Adding these percentages gives 100%, confirming that all applicants are accounted for.

Quiz 2: Displaying and Describing Categorical Data

Of the 1606 applicants to a college program,456 were Black or Hispanic,300 were Asian,and 850 were White.Summarize the relative frequency distribution of ethnicity with a sentence or two in the proper context.

Of the 1470 applicants to a college program,760 were accepted,269 were wait-listed,and 441 were turned away for lack of space.Find the relative frequency distribution of the decisions made,and write a sentence describing it.