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Essentials of Statistics Study Set 1
Exam 2: Summarizing and Graphing Data
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Question 1
Multiple Choice
A nurse measured the blood pressure of each person who visited her clinic. Following is a relative-frequency histogram for the systolic blood pressure readings for those people aged between 25 and 40. The blood pressure readings were given to the nearest whole number. Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading between 110 and 139 inclusive?
Question 2
Multiple Choice
A store manager counts the number of customers who make a purchase in his store each day. The data are as follows.
5
6
3
9
2
5
5
6
3
2
\begin{array} { l l l l l l l l l l } 5 & 6 & 3 & 9 & 2 & 5 & 5 & 6 & 3 & 2\end{array}
5
6
3
9
2
5
5
6
3
2
Question 3
Multiple Choice
A car dealer is deciding what kinds of vehicles he should order from the factory. He looks at his sales report for the preceding period. Choose the vertical scale so that the relative frequencies are represented.
Vehicle
Sales
Economy
30
Sports
7.5
Family
52.5
Luxury
15
Truck
45
\begin{array} { r | r } \text { Vehicle } & \text { Sales } \\\hline \text { Economy } & 30 \\\text { Sports } & 7.5 \\\text { Family } & 52.5 \\\text { Luxury } & 15 \\\text { Truck } & 45\end{array}
Vehicle
Economy
Sports
Family
Luxury
Truck
Sales
30
7.5
52.5
15
45
Construct a Pareto chart to help him decide.
Question 4
Essay
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.
6
6
6
4
6
6
9
8
6
3
8
6
6
8
6
6
8
6
6
8
6
8
8
4
\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}
6
6
6
8
6
6
4
6
6
8
6
6
9
6
8
8
6
6
3
8
8
8
6
4
Construct a frequency distribution. Use 4 classes, a class width of 2 hours, and a lower limit of 3 for class 1.
Hours
Frequency
\begin{array}{l|l}\text { Hours } & \text { Frequency } \\\hline &\end{array}
Hours
Frequency
Question 5
Essay
In a survey, 20 people were asked how many magazines they had purchased during the previous year. The results are shown below. Construct a histogram to represent the data. Use 4 classes with a class width of 10, and begin with a lower class limit of -0.5. What is the approximate amount at the center?
6
15
3
36
25
18
12
18
5
30
24
7
0
22
33
24
19
4
12
9
\begin{array} { r r r r r r r r r r } 6 & 15 & 3 & 36 & 25 & 18 & 12 & 18 & 5 & 30 \\24 & 7 & 0 & 22 & 33 & 24 & 19 & 4 & 12 & 9\end{array}
6
24
15
7
3
0
36
22
25
33
18
24
12
19
18
4
5
12
30
9
Question 6
Multiple Choice
The frequency distribution below summarizes the home sale prices in the city of Summerhill for the month of June. Determine the width of each class.
(Sale price in thousand $)
Frequency
80.0
−
110.9
2
111.0
−
141.9
5
142.0
−
172.9
7
173.0
−
203.9
10
204.0
−
234.9
3
235.0
−
265.9
1
\begin{array} { c | c } \text { (Sale price in thousand \$) } & \text { Frequency } \\\hline 80.0 - 110.9 & 2 \\111.0 - 141.9 & 5 \\142.0 - 172.9 & 7 \\173.0 - 203.9 & 10 \\204.0 - 234.9 & 3 \\235.0 - 265.9 & 1\end{array}
(Sale price in thousand $)
80.0
−
110.9
111.0
−
141.9
142.0
−
172.9
173.0
−
203.9
204.0
−
234.9
235.0
−
265.9
Frequency
2
5
7
10
3
1
Question 7
Multiple Choice
The histogram below represents the number of television sets per household for a sample of U.S. households. How many households are included in the histogram?
Question 8
Multiple Choice
Sturges' guideline suggests that when constructing a frequency distribution, the ideal number of classes can be approximated by
1
+
(
log
n
)
/
(
log
2
)
1 + ( \log n ) / ( \log 2 )
1
+
(
lo
g
n
)
/
(
lo
g
2
)
where n is the number of data values. Use this Guideline to find the ideal number of classes when the number of data values is 180.
Question 9
Multiple Choice
x
0.21
0.06
0.58
0.14
0.31
0.64
0.5
0.39
y
0.64
0.58
0.91
0.31
−
0.59
0.95
0.97
−
0.26
\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}
x
y
0.21
0.64
0.06
0.58
0.58
0.91
0.14
0.31
0.31
−
0.59
0.64
0.95
0.5
0.97
0.39
−
0.26
Question 10
Essay
Suppose you are comparing frequency data for two different groups, 25 managers and 150 blue collar workers. Why would a relative frequency distribution be better than a frequency distribution?
Question 11
Short Answer
The histogram below shows the distribution of the assets (in millions of dollars) of 71 companies. Does the distribution appear to be normal?
Question 12
Multiple Choice
Use the given paired data to construct a scatterplot. -
x
−
5
−
7
−
2
−
4
2
5
1
7
−
4
−
1
y
3
−
6
1
3
4
−
2
−
2
1
−
7
−
4
\begin{array}{lllllllllll}x & -5 & -7 & -2 & -4 & 2 & 5 & 1 & 7 & -4 & -1 \\y & 3 & -6 & 1 & 3 & 4 & -2 & -2 & 1 & -7 & -4\end{array}
x
y
−
5
3
−
7
−
6
−
2
1
−
4
3
2
4
5
−
2
1
−
2
7
1
−
4
−
7
−
1
−
4
Question 13
Essay
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?