Question 1

The table contains the frequency and relative-frequency distributions for the ages of the employees in a particular company department. $\begin{array}{c|c|c} \text { Age (years) } & \text { Frequency } & \text { Relative frequency } \ \hline 20 \text {-under 30 } & 3 & 0.1875 \ 30 \text {-under 40 } & 6 & 0.375 \ 40 \text {-under 50 } & 4 & 0.25 \ 50 \text {-under 60 } & 1 & 0.0625 \ 60 \text {-under 70 } & 2 & 0.125 \end{array}$

Accepted Answer

The answer of The table contains the frequency and relative-frequency...

Question 2

Construct the requested histogram.
-The table below shows the number of days off in a given year for 30 police detectives. $\begin{array}{l} \begin{array} { r | c | c }  \text { Days off } & \text { Frequency } & \text { Relative frequency } \ \hline \text { 0-under 2 } & 10 & 0.333 \ \text { 2-under 4 } & 1 & 0.033 \ \text { 4-under 6 } & 1 & 0.233 \ \text { 6-under 8 } & 7 & 0.233 \ \text { 8-under 10 } & 1 & 0.033 \ \text { 10-under 12 } & 4 & 0.133 \end{array}\\ \text { Construct a relative-frequency histogram. } \end{array}$

Accepted Answer

The answer of Construct the requested histogram.
-The table below shows...

Question 3

Use cutpoint grouping to organize these data into a frequency distribution.
-Lori asked 24 students how many hours they had spent doing homework during the previous week. The results are shown below. $\begin{array} { r r r r r r r r r r r r } 11 & 10 & 11 & 9 & 11 & 11 & 14 & 12 & 11 & 8 & 12 & 10 \ 10 & 12 & 11 & 10 & 12 & 11 & 10 & 12 & 10 & 12 & 12 & 9 \end{array}$ Construct a frequency distribution. Use 4 classes, a class width of 2 hours, and a lower limit of 8 for the first class. $\begin{array}{l|l} \text { Hours } & \text { Frequency } \ \hline & \ & \end{array}$

Accepted Answer

$$\begin{array} { r | r } 
\ { \text { Hours } } & \text { Frequency } \
\hline 8 \text {-under } 10 & 3 \
\text { 10-under } 12 & 13 \
\text { 12-under } 14 & 7 \
\text { 14-under } 16 & 1
\end{array}$$

Question 4

Use cutpoint grouping to organize these data into a frequency distribution.
-Kevin asked some of his friends how many hours they had worked during the previous week at their after-school jobs. The results are shown below.  $$\begin{array} { l l l l l l l l l l l l } 
6 & 6 & 6 & 4 & 6 & 6 & 9 & 8 & 6 & 4 & 8 & 6 \
6 & 8 & 6 & 6 & 8 & 6 & 6 & 8 & 6 & 8 & 8 & 4
\end{array}$$  Construct a frequency distribution. Use 4 classes, a class width of 2 hours, and a lower limit of 3 for the first class. 
$\begin{array}{l|l}
\text { Hours } & \text { Frequency } \
\hline
\end{array}$

Accepted Answer

The answer of Use cutpoint grouping to organize these data...

Question 5

A television manufacturer sold three times as many televisions in 1995 as it did in 1985. To illustrate this fact, the manufacturer draws a pictogram as shown below. The television on the right is three times as tall and three times as wide as the television on the left.  This pictogram is misleading because it actually gives the visual impression that nine times as many televisions were sold in 2005 as in 1995. How can the manufacturer correctly illustrate the fact that sales in 2005 were three times sales in 1995?

Accepted Answer

The answer of A television manufacturer sold three times as...

Question 6

Given the following "data scenario," decide which type of grouping (single-value, limit, or cutpoint) is probably the best.
-Number of Pets: The number of pets per family.

Accepted Answer

Single-value grouping is most appropriate for the number of pets per family because it allows for a clear, discrete count of pets in each family, which is typically a small, whole number.

Question 7

The bar graph below shows the average cost of renting a studio in one city in each of the years 2002 through 2006.  By what percentage does the average price increase from 2002 to 2003? Obtain a truncated version of the graph by sliding a piece of paper over the bottom of the graph so that the bars start at 300. In the truncated graph, by what percentage does the price appear to increase from 2002 to 2003? Why is the truncated graph misleading?

Accepted Answer

The answer of The bar graph below shows the average...

Question 8

Use cutpoint grouping to organize these data into a frequency distribution.
-On a math test, the scores of 24 students were $$\begin{array} { l l l l l l l l l l l l } 
93 & 72 & 71 & 62 & 71 & 71 & 93 & 87 & 71 & 61 & 85 & 72 \
72 & 85 & 71 & 72 & 85 & 71 & 72 & 87 & 72 & 85 & 87 & 62
\end{array}$$  Construct a frequency distribution. Use 4 classes beginning with a lower class limit of 60 . 
$\begin{array}{l|l} \text { Score } & \text { Frequency } \ \hline & \ & \end{array}$

Accepted Answer

The answer of Use cutpoint grouping to organize these data...

Question 9

Given the following "data scenario," decide which type of grouping (single-value, limit, or cutpoint) is probably the best.
-Exam Scores: The exam scores, rounded to the nearest whole number, of all students in a given math course.

Accepted Answer

Limit grouping is used when the data is continuous and has a wide range of values. In this case, the exam scores are continuous and range from 0 to 100, so limit grouping is the best choice.

Question 10

Maria constructed the frequency distribution shown below. The data represent the heights of 60 randomly selected women. $$\begin{array} { c c }  \text { Height } & \text { Frequency } \ \hline 54 \text {-under 60 } & 7 \ \text { 60-under 61 } & 1 \ \text { 61-under 62 } & 3 \ \text { 62-under 63 } & 5 \ \text { 63-under 64 } & 7 \ \text { 64-under 65 } & 7 \ \text { 65-under 66 } & 6 \ 66 \text {-under } 72 & 24 \end{array}$$ She concluded from her frequency distribution that the heights 66, 67, 68, 69, 70, and 71 inches are the most common for women. What is wrong with her conclusion? How is her frequency distribution misleading and how could the table be improved?

Accepted Answer

The answer of Maria constructed the frequency distribution shown below....

Question 11

When organizing data into tables, what is the disadvantage of having too many classes? What is the disadvantage of having too few classes?

Accepted Answer

The answer of When organizing data into tables, what is...

Question 12

Which type of graph, a stem-and-leaf diagram or a frequency histogram, would be more useful for the data set below? Explain your thinking. $$\begin{array} { r r c r c c c c r }  2.3 & 3.2 & 5.1 & 6.3 & 7.3 & 7.7 & 8.1 & 8.9 & 9.3 \ 9.5 & 10.2 & 11.1 & 12.7 & 14.7 & 15.6 & 16.4 & 18.6 & 19.1 \end{array}$$

Accepted Answer

The answer of Which type of graph, a stem-and-leaf diagram...

Question 13

Give an example of a data set whose distribution is likely to be bimodal. Describe the population from which the sample is selected and the variable that is measured for each person. Explain why you think the distribution will be bimodal.

Accepted Answer

The answer of Give an example of a data set...

Question 14

Construct the requested histogram.
-The table gives the frequency distribution for the data involving the number of radios per household for a sample of 80 U.S. households.  $\begin{array} { c | c } 
\text { \# of Radios } & \text { Frequency } \
\hline 1 & 5 \
2 & 10 \
3 & 30 \
4 & 25 \
5 & 10
\end{array}$ 
$\text { Construct a relative frequency histogram. }$

Accepted Answer

The answer of Construct the requested histogram.
-The table gives the...

Question 15

For a given data set, why might a researcher prefer to study organized data rather than the original data? Can you think of any circumstances in which a researcher may prefer to use the original data rather than organized data?

Accepted Answer

The answer of For a given data set, why might...

Question 16

A television manufacturer sold three times as many televisions in 2005 as it did in 1995. To illustrate this fact, the manufacturer draws a pictogram as shown below. The television on the right is three times as tall and three times as wide as the television on the left.  Why is this pictogram misleading? What visual impression is portrayed by the pictogram?

Accepted Answer

The answer of A television manufacturer sold three times as...

Question 17

Use limit grouping to organize these data into a frequency distribution.
-Kevin asked some of his friends how many hours they had worked during the previous week at their after-school jobs. The results are shown below. $$\begin{array} { l l l l l l l l l l l l }  6 & 5 & 6 & 3 & 6 & 6 & 9 & 8 & 6 & 4 & 8 & 5 \ 5 & 8 & 6 & 5 & 8 & 6 & 5 & 8 & 5 & 8 & 8 & 3 \end{array}$$ 
Construct a frequency distribution. Use 4 classes, a class width of 2 hours, and a lower limit of 3 for the first class. 
$\begin{array}{l|l} \text { Hours } & \text { Frequency } \ \hline & \ & \end{array}$

Accepted Answer

The answer of Use limit grouping to organize these data...

Question 18

Provide an appropriate response.
-The preschool children at Elmwood Elementary School were asked to name their favorite color. The results are listed below. Construct a frequency distribution and a relative frequency distribution. $$\begin{array} { c c c c c }  \text { blue } & \text { blue } & \text { red } & \text { green } & \text { purple } \ \text { purple } & \text { purple } & \text { blue } & \text { purple } & \text { red } \ \text { purple } & \text { red } & \text { green } & \text { green } & \text { green } \ \text { red } & \text { purple } & \text { green } & \text { purple } & \text { yellow } \end{array}$$

Accepted Answer

The answer of Provide an appropriate response.
-The preschool children at...

Question 19

Given the following "data scenario," decide which type of grouping (single-value, limit, or cutpoint) is probably the best.
-Wingspan of Cardinal: The wingspan lengths, to the nearest hundredth of a millimeter, of a sample of 35 cardinals.

Accepted Answer

Cutpoint grouping is most suitable for continuous data measured precisely, such as wingspan lengths to the nearest hundredth of a millimeter. This method allows for the creation of intervals that can effectively categorize the continuous range of measurements.

Question 20

Suppose that you wish to construct a stem-and-leaf diagram for the data set below. What would the stems be? $$\begin{array} { r r r r r r r r r }  98 & 103 & 146 & 118 & 92 & 128 & 135 & 141 & 136 \ 143 & 126 & 111 & 109 & 97 & 124 & 147 & 114 & 119 \ 140 & 122 & 92 & 130 & 101 & 148 & 138 & 90 & 123 \end{array}$$

Accepted Answer

The answer of Suppose that you wish to construct a...

Quiz 2: Organizing Data

Given the following "data scenario," decide which type of grouping (single-value, limit, or cutpoint) is probably the best. -Number of Pets: The number of pets per family.

Given the following "data scenario," decide which type of grouping (single-value, limit, or cutpoint) is probably the best. -Exam Scores: The exam scores, rounded to the nearest whole number, of all students in a given math course.

When organizing data into tables, what is the disadvantage of having too many classes? What is the disadvantage of having too few classes?

Give an example of a data set whose distribution is likely to be bimodal. Describe the population from which the sample is selected and the variable that is measured for each person. Explain why you think the distribution will be bimodal.

For a given data set, why might a researcher prefer to study organized data rather than the original data? Can you think of any circumstances in which a researcher may prefer to use the original data rather than organized data?

Given the following "data scenario," decide which type of grouping (single-value, limit, or cutpoint) is probably the best. -Wingspan of Cardinal: The wingspan lengths, to the nearest hundredth of a millimeter, of a sample of 35 cardinals.