Question 1

Use the given data to construct 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. $$\begin{array} { l l l l l l l l l l l l } 
6 & 6 & 6 & 4 & 6 & 6 & 9 & 8 & 6 & 3 & 8 & 6 \
6 & 8 & 6 & 6 & 8 & 6 & 6 & 8 & 6 & 8 & 8 & 4
\end{array}$$
Construct a frequency distribution. Use 4 classes, a class width of 2 hours, and a lower limit of 3 for class 1.
$\begin{array}{l|l}
\text { Hours } & \text { Frequency } \
\hline &
\end{array}$

Accepted Answer

The answer of Use the given data to construct a...

Question 2

Histograms and Pareto charts are both bar charts. What is the significant difference between the two?

Accepted Answer

The answer of Histograms and Pareto charts are both bar...

Question 3

Use the given data to construct a frequency distribution.
-The following figures represent Jennifer's monthly charges for long distance telephone calls for the past twelve months. 
$$\begin{array} { r r r r } 
7.33 & 11.26 & 13.54 & 17.00 \
10.56 & 16.15 & 9.59 & 15.08 \
14.50 & 15.28 & 14.88 & 12.41
\end{array}$$
Construct a frequency distribution with 4 classes.
$\begin{array}{l|l}
\text { Charges } & \text { Frequency } \
\hline &\\\
\end{array}$

Accepted Answer

The answer of Use the given data to construct a...

Question 4

The 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 second version of the graph by sliding a piece of paper over the bottom of the graph so that the bars start at 300. In this new graph, by what percentage does the price appear to increase from 2002 to 2003? Is the second graph misleading?

Accepted Answer

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

Question 5

Use the high closing values of Naristar Inc. stock from the years $1990 - 2001$ to construct a time-series graph. (Let $x = 0$ represent 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 Use the high closing values of Naristar...

Question 6

The frequency table below shows the number of days off in a given year for 30 police detectives. 
$$\begin{array} { r | c } 
\text { Days off } & \text { Frequency } \
\hline 0 - 2 & 10 \
3 - 5 & 1 \
6 - 8 & 7 \
9 - 11 & 7 \
12 - 14 & 1 \
15 - 17 & 4
\end{array}$$ 
Construct a histogram. Use the class midpoints for the horizontal scale. Does the result appear to be a normal distribution? Why or why not?

Accepted Answer

The answer of The frequency table below shows the number...

Question 7

The following frequency distribution analyzes the scores on a math test. Find the class boundaries of scores interval 40-59. 
$$\begin{array} { c c } 
\hline \text { Scores } & \text { Number of students } \
\hline 40 - 59 & 2 \
60 - 75 & 4 \
76 - 82 & 6 \
83 - 94 & 15 \
95 - 99 & 5 \
\hline
\end{array}$$

Accepted Answer

Class boundaries are found by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of the class interval. For the interval 40-59, the boundaries are 39.5 and 59.5.

Question 8

Use the given data to construct a frequency distribution.
-A school district performed a study to find the main causes leading to its students dropping out of school. Thirty cases were analyzed, and a primary cause was assigned to each case. The causes included unexcused absences (U), illness (I), family problems (F), and other causes (O). The results for the thirty cases are listed below:
 $\begin{array} { c c c c c c c c c c } \mathrm { U } & \mathrm { U } & \mathrm { U } & \mathrm { I } & \mathrm { F } & \mathrm { O } & \mathrm { O } & \mathrm { U } & \mathrm { I } & \mathrm { F } \ \mathrm { F } & \mathrm { O } & \mathrm { U } & \mathrm { I } & \mathrm { I } & \mathrm { F } & \mathrm { I } & \mathrm { I } & \mathrm { O } & \mathrm { U } \ \mathrm { I } & \mathrm { F } & \mathrm { F } & \mathrm { U } & \mathrm { U } & \mathrm { I } & \mathrm { I } & \mathrm { O } & \mathrm { F } & \mathrm { U } \end{array}$
Construct a table summarizing the frequency distribution of the primary causes leading to student dropout.
$\begin{array}{l|l}
\text { Cause } & \text { Frequency } \
\hline & \
&
\end{array}$

Accepted Answer

The answer of Use the given data to construct a...

Question 9

The graph below shows the number of car accidents occurring in one city in each of the years 2001 through 2006. The number of accidents dropped in 2003 after a new speed limit was imposed. Does the graph distort the data? How would you redesign the graph to be less misleading?

Accepted Answer

The answer of The graph below shows the number of...

Question 10

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 Suppose that you construct a histogram and...

Question 11

The frequency table below shows the amount of weight loss during the first month of a diet program for a group of men. Constructing a frequency polygon. Applying a loose interpretation of the requirements for a normal distribution, do the pounds of weight loss appear to be normally distributed?
Why or why not? $$\begin{array} { c | c } 
\text { Weight (lb) } & \text { Frequency } \
\hline 5 - 7 & 2 \
8 - 10 & 9 \
11 - 13 & 18 \
14 - 16 & 13 \
17 - 19 & 4 \
20 - 22 & 1
\end{array}$$

Accepted Answer

The answer of The frequency table below shows the amount...

Question 12

Construct a frequency distribution that includes an outlier. Construct the corresponding histogram. Then, construct the corresponding histogram without including the outlier.
How much does the outlier affect the shape of the histogram?

Accepted Answer

The answer of Construct a frequency distribution that includes an...

Question 13

Use the given paired data to construct a scatterplot.
-$\begin{array}{lccccccccc}
x & -4 & 2 & 8 & 10 & 12 & 8 & 5 & -3 & -2 \
y & 3 & 7 & 11 & 10 & 9 & 6 & 7 & 3 & 2
\end{array}$

Accepted Answer

The answer of Use the given paired data to construct...

Question 14

Construct a frequency distribution 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 Construct a frequency distribution and the corresponding...

Question 15

The histogram below shows the distribution of the assets (in millions of dollars) of 71 companies. Does the distribution appear to be normal?

Accepted Answer

The answer of The histogram below shows the distribution of...

Question 16

Consider the frequency distribution below, which has single values as classes:
 $$\begin{array} { c | c } 
\text { Value } & \text { Frequency } \
\hline 10 & 1 \
11 & 3 \
12 & 7 \
13 & 18 \
14 & 10 \
15 & 4 \
16 & 2 \
17 & 7 \
18 & 16 \
19 & 10 \
20 & 6 \
21 & 2
\end{array}$$
 Describe the distribution of the data. Use this frequency distribution to create two new frequency distributions for the data, one with four classes of equal width and one with six classes of equal width. Does the frequency distribution with four classes capture the distribution of the data? Does the frequency distribution with six classes capture the distribution of the data? Explain your thinking.

Accepted Answer

The answer of Consider the frequency distribution below, which has...

Question 17

Suppose that a data set has a minimum value of 18 and a maximum of 83 and that you want 5 classes. Explain how to find the class width for this frequency table. What happens if you mistakenly use a class width of 13 instead of 14?

Accepted Answer

The answer of Suppose that a data set has a...

Question 18

Use the given data to construct a frequency distribution.
-Lori asked 24 students how many hours they had spent doing homework during theprevious week. The results are shown below. 
$\begin{array} { l l l l l l l l l l l l } 11 & 10 & 11 & 8 & 11 & 11 & 15 & 13 & 11 & 8 & 13 & 10 \10 & 13 & 11 & 10 & 13 & 11 & 10 & 13 & 10 & 13 & 13 & 8 \end{array}$
Construct a frequency distribution. Use 4 classes, a class width of 2 hours, and a lower limit of 8 for
$\begin{array}{l|l}
\text { Hours } & \text { Frequency } \
\hline &
\end{array}$

Accepted Answer

The answer of Use the given data to construct a...

Question 19

Consider the frequency distribution 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 distribution for this data with 4 classes. Now, construct another frequency distribution 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 distributions. 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 Consider the frequency distribution below, which has...

Question 20

$\begin{array}{ccccccccc}
\mathrm{x} & 0.21 & 0.06 & 0.58 & 0.14 & 0.31 & 0.64 & 0.5 & 0.39 \
\text { y } & 0.64 & 0.58 & 0.91 & 0.31 & -0.59 & 0.95 & 0.97 & -0.26
\end{array}$

Accepted Answer

The answer of \(\begin{array}{ccccccccc}
\mathrm{x} & 0.21 & 0.06 & 0.58...

Quiz 2: Summarizing and Graphing Data

Histograms and Pareto charts are both bar charts. What is the significant difference between the two?

The graph below shows the number of car accidents occurring in one city in each of the years 2001 through 2006. The number of accidents dropped in 2003 after a new speed limit was imposed. Does the graph distort the data? How would you redesign the graph to be less misleading?

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?

Construct a frequency distribution that includes an outlier. Construct the corresponding histogram. Then, construct the corresponding histogram without including the outlier. How much does the outlier affect the shape of the histogram?

Use the given paired data to construct a scatterplot. - x−428101285−3−2y37111096732\begin{array}{lccccccccc}x & -4 & 2 & 8 & 10 & 12 & 8 & 5 & -3 & -2 \\y & 3 & 7 & 11 & 10 & 9 & 6 & 7 & 3 & 2\end{array}xy​−43​27​811​1010​129​86​57​−33​−22​

The histogram below shows the distribution of the assets (in millions of dollars) of 71 companies. Does the distribution appear to be normal?

Suppose that a data set has a minimum value of 18 and a maximum of 83 and that you want 5 classes. Explain how to find the class width for this frequency table. What happens if you mistakenly use a class width of 13 instead of 14?