Question 1

Provide an appropriate response.
-Construct a frequency table and the corresponding histogram in which the following conditions are satisfied:
- The frequency for the second class is twice the frequency of the first class
- In the histogram, the area of the bar corresponding to the second class is four times the area of the bar corresponding to the first class

Accepted Answer

The answer of Provide an appropriate response.
-Construct a frequency table...

Question 2

Provide an appropriate response.
-Shortly before a mayoral election, a market research firm took a poll to find out which candidate people were planning to vote for. The results are shown below.
 $$\begin{array} { l | c } 
\text { Candidate } & \text { Frequency } \
\hline \text { Li Fong } & 2120 \
\text { Bob Green } & 2329 \
\text { Sue Moore } & 1042 \
\text { Jose Alvarez } & 399
\end{array}$$ 
You wish to construct a graph to represent the data. It should be easy to see from your graph which candidate is in the lead. Which graph would be more useful, a bar graph or a pie chart? Explain your thinking.

Accepted Answer

The answer of Provide an appropriate response.
-Shortly before a mayoral...

Question 3

Solve the problem.
-The following data show the number of laps run by each participant in a marathon.
$\begin{array} { l l l l l l l l l l l l } 46 & 65 & 55 & 43 & 51 & 48 & 57 & 30 & 43 & 49 & 32 & 56 \end{array}$
Use the data to construct a stem-and-leaf plot.
A)
$\begin{array}{l|l}
3 & 02 \
4 & 3689 \
4 & 13567 \
6 & 5
\end{array}$

B)
$\begin{array}{l|l}
3 & 02 \
4 & 3689 \
5 & 13567 \
6 & 5
\end{array}$

C)
$\begin{array}{l|l}
3 & 02 \
4 & 33689 \
5 & 1567 \
6 & 5
\end{array}$

D)
$\begin{array}{l|l}
3 & 02 \
4 & 689 \
5 & 133567 \
6 & 5
\end{array}$

Accepted Answer

The answer of Solve the problem.
-The following data show the...

Question 4

Solve the problem.
-The weights of 22 members of the varsity football team are listed below.
 $\begin{array}{lllllllllll}
144 & 152 & 142 & 151 & 160 & 152 & 131 & 164 & 141 & 153 & 140 \
144 & 175 & 156 & 147 & 133 & 172 & 159 & 135 & 159 & 148 & 171
\end{array}$

A)
$\begin{array} { l | l l } 
13 & 135 \
14 & 1223699 \
15 & 0124478 \
16 & 04 \
17 & 125
\end{array}$

B)
$\begin{array}{l|l}
13 & 135 \
14 & 012478 \
15 & 12369 \
16 & 04 \
17 & 125
\end{array}$

C)
$\begin{array}{l|l}
13 & 135 \
14 & 0124478 \
15 & 122369 \
16 & 04 \
17 & 125
\end{array}$

D)
$\begin{array}{l|l}
13 & 135 \
14 & 0124478 \
15 & 1223699 \
16 & 04 \
17 & 125
\end{array}$

Accepted Answer

The correct answer is determined by organizing the weights into a stem-and-leaf plot. Each stem represents the tens place, and the leaves represent the ones place of the weights. The plot must accurately reflect the distribution of the weights. Option D correctly organizes all the weights into their respective stems and leaves, matching the given data.

Question 5

Provide an appropriate response.
-Explain the difference between a frequency distribution and a relative frequency distribution. Comment on the differences on the vertical axis scale. Given the same data set and the same classes, will the shapes of the frequency distribution and the relative frequency distribution be the same? You may draw a diagram to support your answer.

Accepted Answer

The answer of Provide an appropriate response.
-Explain the difference between...

Question 6

Provide an appropriate response.
-Suppose that you construct a histogram and a relative frequency histogram corresponding to a particular frequency table. In what ways will the two histograms be similar? In what ways will they differ?

Accepted Answer

The answer of Provide an appropriate response.
-Suppose that you construct...

Question 7

Solve the problem.
-The attendance counts for this season's basketball games are listed below.
$\begin{array} { l l l l } 227 & 239 & 215 & 219 \end{array}$
$\begin{array} { l l l l } 221 & 233 & 229 & 233 \end{array}$
$\begin{array} { l l l l } 235 & 228 & 245 & 231 \end{array}$
Use the data to construct a stem-and-leaf plot.
A)
$\begin{array}{l|l}
21 & 579 \
22 & 189 \
23 & 1359 \
24 & 5
\end{array}$

B)
$\begin{array}{l|l}
21 & 59 \
22 & 189 \
23 & 1359 \
24 & 5
\end{array}$

C)
$\begin{array}{l|l}
21 & 59 \
22 & 1789 \
23 & 13359 \
24 & 5
\end{array}$

D)
$\begin{array} { l | l } 
21 & 579 \
22 & 189 \
23 & 13359 \
24 & 5
\end{array}$

Accepted Answer

The answer of Solve the problem.
-The attendance counts for this...

Question 8

Provide an appropriate response.
-Suppose that you want to construct a pie chart to represent the following data. 
$$\begin{array} { l | c } 
\text { Blood Type } & \text { Frequenc } \
\hline \mathrm { O } & 90 \
\mathrm {~A} & 84 \
\mathrm {~B} & 18 \
\mathrm { AB } & 8
\end{array}$$ 
Explain how you would calculate the angle for the pie-shaped piece corresponding to the blood type O.

Accepted Answer

The answer of Provide an appropriate response.
-Suppose that you want...

Question 9

Provide an appropriate response.
-Suppose that a histogram is constructed for the frequency table shown below:
 $$\begin{array} { c | c } 
\text { Age } & \text { Frequency } \
\hline 30 - 39 & 11 \
40 - 49 & 23 \
50 - 59 & 17 \
60 - 69 & 12 \
70 - 89 & 6
\end{array}$$ 
The class 60-69 has twice the frequency of the class 70-89. In the histogram, will the area of the bar for the class 60-69 be twice the area of the bar for the class 70-89? In other words, will areas be proportional to frequencies in this histogram? Explain your thinking. Are there any conditions under which areas are proportional to frequencies in histograms?

Accepted Answer

The answer of Provide an appropriate response.
-Suppose that a histogram...

Question 10

A machine is supposed to fill juice bottles with 16 fluid ounces of juice. The manufacturer picks a sample of bottles which have been filled by the machine and determines the volume of juice in each bottle. The results are shown in the stem-and-leaf diagram below. The leaf unit is 0.1. $$\begin{array} { l | l } 
15 & 1 \
15 & 3 \
15 & 45 \
15 & 667777 \
15 & 888899999 \
16 & 000000011111 \
16 & 222223333 \
16 & 445 \
16 & 66 \
16 & 8
\end{array}$$
How many bottles were sampled?
A)46
B)16
C)44
D)10

Accepted Answer

The answer of A machine is supposed to fill juice...

Question 11

Solve the problem.
-The midterm test scores for the seventh-period typing class are listed below.
$\begin{array} { l l l l l l l l l l l l l l l l } 85 & 77 & 93 & 91 & 74 & 65 & 68 & 97 & 88 & 59 & 74 & 83 & 85 & 72 & 63 & 79 \end{array}$
Use the data to construct a stem-and-leaf plot.
A)
$\begin{array}{l|l}
5 & 9 \
6 & 358 \
7 & 3558 \
8 & 24479 \
9 & 137
\end{array}$

B)
$\begin{array}{l|l}
5 & 9 \
6 & 358 \
7 & 3558 \
8 & 2479 \
9 & 137
\end{array}$

C)
$\begin{array}{l|l}
5 & 9 \
6 & 358 \
7 & 2479 \
8 & 358 \
9 & 137
\end{array}$

D)
$\begin{array}{l|l}
5 & 9 \
6 & 358 \
7 & 24479 \
8 & 3558 \
9 & 137
\end{array}$

Accepted Answer

The answer of Solve the problem.
-The midterm test scores for...

Question 12

A machine is supposed to fill juice bottles with 16 fluid ounces of juice. The manufacturer picks a sample of bottles which have been filled by the machine and determines the volume of juice in each bottle. The results are shown in the stem-and-leaf diagram below. The leaf unit is 0.1. $$\begin{array} { l | l } 
15 & 1 \
15 & 3 \
15 & 45 \
15 & 667777 \
15 & 888899999 \
16 & 00000011111 \
16 & 222223333 \
16 & 445 \
16 & 66 \
16 & 8
\end{array}$$
What is the smallest volume of juice (in fluid ounces)measured for the bottles sampled?
A)15 fluid ounces
B)151 fluid ounces
C)15.1 fluid ounces
D)16 fluid ounces

Accepted Answer

The smallest volume of juice measured, according to the stem-and-leaf diagram, is 15.1 fluid ounces. The stem represents the whole number part (15), and the smallest leaf (1) represents the decimal part (0.1), making the smallest volume 15.1 fluid ounces.

Question 13

The stem-and-leaf diagram below shows the highest wind velocity ever recorded in 30 different U.S. cities. The velocities are given in miles per hour. The leaf unit is 1.0. $$\begin{array} { l | l } 
6 & 4 \
7 & 23 \
7 & 589 \
8 & 0111344 \
8 & 5568899 \
9 & 0012234 \
9 & 559
\end{array}$$
What is the highest wind velocity recorded in these cities?
A)9.9 miles per hour
B)9.5 miles per hour
C)95 miles per hour
D)99 miles per hour

Accepted Answer

The highest wind velocity recorded is represented by the "9" in the stem and "9" in the leaf, combining to form "99". This means the highest wind velocity is 99 miles per hour.

Question 14

Provide an appropriate response.
-Consider the frequency table below which has single values as classes:
 $$\begin{array} { c | c } 
\text { Value } & \text { Frequency } \
\hline 10 & 1 \
11 & 3 \
12 & 7 \
13 & 18 \
14 & 10 \
15 & 4 \
16 & 2 \
17 & 7 \
18 & 16 \
19 & 10 \
20 & 6 \
21 & 2
\end{array}$$ 
Construct a new frequency table for this data with 4 classes. Now construct another frequency table for this data with 6
classes. Suppose that you construct a histogram corresponding to the original data and histograms corresponding to
each of the new frequency tables. Describe the shapes of the three histograms. Does the histogram with six classes
capture the distribution of the data? Does the histogram with four classes capture the distribution of the data?

Accepted Answer

The answer of Provide an appropriate response.
-Consider the frequency table...

Question 15

Solve the problem.
-Twenty-four workers were surveyed about how long it takes them to travel to work each day. The data below are given in minutes.
 $\begin{array} { l l l l l l l l l l l l } 20 & 35 & 42 & 52 & 65 & 20 & 60 & 49 & 24 & 37 & 23 & 24 \end{array}$
$\begin{array} { l l l l l l l l l l l l } 22 & 20 & 41 & 25 & 28 & 27 & 50 & 47 & 58 & 30 & 32 & 48 \end{array}$
Use the data to construct a stem-and-leaf plot.
A)
$\begin{array}{l|ll}
2 & 0&0&0&2&3&4&4&5&7 \
3 & 0&2&5&7&8 \
4 & 1&2&7&8&9 \
5 & 0&2&8 \
6 & 0&5
\end{array}$

B)
$\begin{array} { l | l l } 
2 & 0234578 \
3 & 0257 \
4 & 12789 \
5 & 028 \
6 & 05
\end{array}$
C)
$\begin{array}{l|l}
2 & 000234457 \
3 & 0257 \
4 & 12789 \
5 & 028 \
6 & 05
\end{array}$

D)
$\begin{array} { l | l l l } 
2 & 0  23457 \
3 & 02578 \
4 & 12789 \
5 & 028 \
6 & 05
\end{array}$

Accepted Answer

The correct stem-and-leaf plot must accurately represent all the data points, with the stem (tens place) on the left and the leaves (ones place) on the right. Option C correctly organizes all the data points according to their tens and ones places, including the correct number of repetitions for the value 20 (three times).

Question 16

Solve the problem.
-Use the high closing values of Naristar Inc. stock from the years 1992 - 2003 to construct a time-series graph.
(Let x = 0 stand for 1992 and so on...)Identify a trend. $$\begin{array} { c | c | c | c } 
\text { Year } & \text { High } & \text { Year } & \text { High } \
\hline 1992 & 48 & 1998 & 62 \
1993 & 53 & 1999 & 60 \
1994 & 47 & 2000 & 68 \
1995 & 55 & 2001 & 42 \
1996 & 58 & 2002 & 51 \
1997 & 61 & 2003 & 78
\end{array}$$

Accepted Answer

The answer of Solve the problem.
-Use the high closing values...

Question 17

Provide an appropriate response.
-Explain in your own words the difference between a bar graph and a histogram. Give an example of data for which you might use a histogram and an example of data for which you might use a bar graph.

Accepted Answer

The answer of Provide an appropriate response.
-Explain in your own...

Question 18

Provide an appropriate response.
-Suppose that you want to construct a graph to represent the following data. 
$$\begin{array} { l | c } 
\text { Blood Type } & \text { Frequency } \
\hline \mathrm { O } & 90 \
\mathrm {~A} & 84 \
\mathrm {~B} & 18 \
\mathrm { AB } & 8
\end{array}$$ 
If you are mostly interested in the number of people in each category as a percentage of the total number of people, would a bar chart or a pie chart be more useful? Explain your thinking.

Accepted Answer

The answer of Provide an appropriate response.
-Suppose that you want...

Question 19

Solve the problem.
-Use the high closing values of Naristar Inc. stock from the years 1990 - 2001 to construct a time-series graph.
(Let x = 0 stand for 1990 and so on...)Identify a trend. $$\begin{array} { c | c | c | c } 
\text { Year } & \text { High } & \text { Year } & \text { High } \
\hline 1990 & 42 & 1996 & 47 \
1991 & 40 & 1997 & 60 \
1992 & 31 & 1998 & 61 \
1993 & 42 & 1999 & 57 \
1994 & 44 & 2000 & 54 \
1995 & 47 & 2001 & 30
\end{array}$$

Accepted Answer

The answer of Solve the problem.
-Use the high closing values...

Question 20

The stem-and-leaf diagram below shows the highest wind velocity ever recorded in 30 different U.S. cities. The velocities are given in miles per hour. The leaf unit is 1.0. 
$$\begin{array} { l | l } 
6 & 4 \
7 & 23 \
7 & 589 \
8 & 0111344 \
8 & 5568899 \
9 & 0012234 \
9 & 559
\end{array}$$
How many of the maximum wind velocities are 85 miles per hour or higher? 
A) 7
B) 18
C) 17
D) 2

Accepted Answer

The stem-and-leaf plot shows wind velocities in miles per hour, with the stem representing the tens place and the leaf representing the ones place. To find velocities of 85 mph or higher, we look for leaves in the "8" stem that are 5 or higher and all leaves in the "9" stem. In the "8" stem, there are 6 velocities (5568899) that are 85 mph or higher, and in the "9" stem, there are 11 velocities (0012234559), making a total of 17 maximum wind velocities of 85 mph or higher.

Quiz 3: Visual Displays of Data

Solve the problem. -The following data show the number of laps run by each participant in a marathon. $\begin{array} { l l l l l l l l l l l l } 46 & 65 & 55 & 43 & 51 & 48 & 57 & 30 & 43 & 49 & 32 & 56 \end{array}$ Use the data to construct a stem-and-leaf plot.

Solve the problem. -The weights of 22 members of the varsity football team are listed below. $\begin{array}{lllllllllll}144 & 152 & 142 & 151 & 160 & 152 & 131 & 164 & 141 & 153 & 140 \\144 & 175 & 156 & 147 & 133 & 172 & 159 & 135 & 159 & 148 & 171\end{array}$

Provide an appropriate response. -Suppose that you construct a histogram and a relative frequency histogram corresponding to a particular frequency table. In what ways will the two histograms be similar? In what ways will they differ?

Solve the problem. -The midterm test scores for the seventh-period typing class are listed below. $\begin{array} { l l l l l l l l l l l l l l l l } 85 & 77 & 93 & 91 & 74 & 65 & 68 & 97 & 88 & 59 & 74 & 83 & 85 & 72 & 63 & 79 \end{array}$ Use the data to construct a stem-and-leaf plot.

Provide an appropriate response. -Explain in your own words the difference between a bar graph and a histogram. Give an example of data for which you might use a histogram and an example of data for which you might use a bar graph.