chapter 2

Question 1

A company collected the ages from a random sample of its middle managers, with the resulting frequency distribution shown below.

Class Interval Frequency
20 to< 25 8
25 to< 30 6
30 to< 35 5
35 to< 40 12
40 to< 45 15
45 to< 50 7

What would be the approximate shape of the relative frequency histogram?

a) uniform
b) skewed to the right
c) skewed to the left
d) linear
e) symmetrical

Answer 1

C) skewed to the left

Explanation
The majority of data lie to the right side of the distribution; the tail of the smaller number of measurements extends to the left, so the graph is skewed with a tail to the left

Question 2

Pareto charts are frequently used to identify ________.

a) random data
b) the cause for extreme skewness to the right
c) the most common types of defects
d) outliers that do not show up on a dot plot

Answer 2

c) the most common types of defects

Explanation
By definition, a defect is a flaw in a population or sample element.

Question 3

An example of manipulating a graphical display to distort reality is ________.

a) starting the axes at zero
b) adding an unbiased caption
c) stretching the axes
d) making the bars in a histogram equal widths

Answer 3

c) stretching the axes

Explanation
Starting the axes at zero is the appropriate method of graphical display, as is making the bars in a histogram equal widths.

Question 4

The number of items rejected daily by a manufacturer because of defects for the last 30 days are:

20, 21, 8, 17, 22, 19, 18, 19, 14, 17, 11, 6, 21, 25, 4, 19, 9, 12, 16, 16, 10, 28, 24, 6, 21, 20, 25, 5, 17, 8

How many classes should be used in constructing a histogram?

a) 6
b) 4
c) 5
d) 8
e) 7

Answer 4

c) 5

Explanation
Number of classes = k, where 2k > 30. So k = 5.

Question 5

Which of the following divides quantitative measurements into classes and graphs the frequency, relative frequency, or percentage frequency for each class?

a) histogram
b) stem-and-leaf display
c) scatter plot
d) dot plot

Answer 5

a) histogram

Explanation
A box plot does not easily group measurements into classes; a scatter plot is for looking at the relationship between two variables.

Question 6

A CFO is looking at what percentage of a company’s resources are spent on computing. He samples companies in the pharmaceutical industry and develops the following stem-and-leaf display (leaf unit = 0.1).

5 269
6 255568999
7 11224557789
8 001222458
9 02455679
10 1556
11 137
12
13 255

What would be the class length used in creating a frequency histogram?

a) 0.9
b) 1.4
c) 1.7
d) 8.3
e) 1.2

Answer 6

b) 1.4

Explanation
There are 50 data measurements. 2k, where k = number of classes and 2k is the closest value larger than 50. 26 = 64, so 6 classes. Class length = (Max value − Min value)/6 = (13.5 − 5.2)/6. Length = 1.38, rounded to 1.4.

Question 7

A CFO is looking at what percentage of a company’s resources are spent on computing. He samples companies in the pharmaceutical industry and develops the following stem-and-leaf display (leaf unit = 0.1).

5 269
6 255568999
7 11224557789
8 001222458
9 02455679
10 1556
11 137
12
13 255

What would be the first class interval for the frequency histogram?

a) 5.2<6.6
b) 5.2<6.4
c) 5.2<6.0
d) 5.0<6.4
e) 5.0<6.0

Answer 7

a) 5.2<6.6

Explanation
There are 50 data measurements. 2k, where k = number of classes and 2k is the closest value larger than 50. 26 = 64, so 6 classes. Class length = (Max value − Min value)/6 = (13.5 − 5.2)/6. Length = 1.38, rounded to 1.4. The boundary for the first nonoverlapping interval is the smallest measurement and the sum of the first measurement and the length (5.2 + 1.38 = 6.58). So the first interval will contain the values 5.2 − 6.5.

Question 8

A CFO is looking at what percentage of a company’s resources are spent on computing. He samples companies in the pharmaceutical industry and develops the following stem-and-leaf display (leaf unit = 0.1).

5 269
6 255568999
7 11224557789
8 001222458
9 02455679
10 1556
11 137
12
13 255

What is the smallest percentage spent on R&D?

a) 5.2
b) 5.6
c) 5.9
d) 50.2
e) 5.02

Answer 8

a) 5.2

Explanation
The smallest value displayed in the graph is 5.2 percent.

Question 9

As a general rule, when creating a stem-and-leaf display, there should be ______ stem values.

a) between 1 and 100
b) between 5 and 20
c) no fewer than 20
d) between 3 and 10

Answer 9

b) between 5 and 20

Explanation
By definition, there should be between 5 and 20 stems to enable a reasonable display of the shape of the distribution.

Question 10

A graphical portrayal of a quantitative data set that divides the data into classes and gives the frequency of each class is a(n) ________.

a) ogive plot
b) Pareto chart
c) dot plot
d) bar chart
e) histogram

Answer 10

e) histogram

Explanation
Pareto and bar charts are used for qualitative data, a dot plot displays individual data points, and an ogive plot is a curved display of the cumulative distribution of the data.

Question 11

A CFO is looking at what percentage of a company’s resources are spent on computing. He samples companies in the pharmaceutical industry and develops the following stem-and-leaf display (leaf unit = 0.1).

5 269
6 255568999
7 11224557789
8 001222458
9 02455679
10 1556
11 137
12
13 255

What is the approximate shape of the distribution of the data?

a) uniform
b) bimodal
c) skewed to the right
d) normal
e) skewed to the left

Answer 11

c) skewed to the right

Explanation
With outliers at the stem of 13 and the majority of the data grouped around stems 6, 7, and 8, the shape is skewed with the outliers to the right.

Question 12

A histogram that has a longer tail extending toward smaller values is ________.

a) a scatter plot
b) skewed to the left
c) skewed to the right
d) normal

Answer 12

b) skewed to the left

Explanation
Smaller values are to the left of the center part of the graph, resulting in a tail to the left. Thus, the graph is skewed to the left.

Question 13

The general term for a graphical display of categorical data made up of vertical or horizontal bars is called a(n) ________.

a) pie chart
b) bar chart
c) Pareto chart
d) ogive plot

Answer 13

b) bar chart

Explanation
An ogive plot is based on quantitative data, a Pareto chart is a specialized bar chart, and a pie chart is a circular graphical display.

Question 14

A CFO is looking at what percentage of a company’s resources are spent on computing. He samples companies in the pharmaceutical industry and develops the following stem-and-leaf display (leaf unit = 0.1).

5 269
6 255568999
7 11224557789
8 001222458
9 02455679
10 1556
11 137
12
13 255

If you were creating a frequency histogram using these data, how many classes would you create?

a) 6
b) 7
c) 4
d) 8
e) 5

Answer 14

a) 6

Explanation
There are 50 data measurements. 2k, where k = number of classes and 2k is the closest value larger than 50. 26 = 64.

Question 15

A ________ displays the frequency of each class with qualitative data and a ________ displays the frequency of each class with quantitative data.

a) bar chart, histogram
b) scatter plot, bar chart
c) histogram, stem-and-leaf display
d) stem-and-leaf, pie chart

Answer 15

a) bar chart, histogram

Explanation
The histogram and stem-and-leaf are used to graphically display quantitative data; a scatter plot is used for displaying the relationship between two variables.

Question 16

If there are 130 values in a data set, how many classes should be created for a frequency histogram?

a) 8
b) 4
c) 5
d) 6
e) 7

Answer 16

a) 8

Explanation
2k, where k = number of classes and 2k is the closest value larger than 130. 27 = 128; 28 = 256.

Question 17

A stem-and-leaf display is best used to ________.

a) display a two-variable treemap.
b) provide a point estimate of the central tendency of the data set
c) display the shape of the distribution
d) provide a point estimate of the variability of the data set

Answer 17

c) display the shape of the distribution

Explanation
It is more difficult to find central tendency and variability using a stem-and-leaf display. It is easy to visualize the shape of the distribution using stem-and-leaf.

Question 18

A company’s Chief Operating Officer (COO) keeps track of the mileage on her trips from her office at corporate headquarters to the company’s off-site manufacturing facility and its nearby suppliers. The stem-and-leaf display of the data for one year is below.

76 9
77 114
78
79 07
80 88
81 2
82 1
83 88

What would be the class length for creating the frequency histogram?
Multiple Choice

a) 9
b) 18
c) 14
d) 27
e) 23

Answer 18

b) 18

Measurements = 12; classes = 4; class length = (838 − 769)/4 = 17.25, rounded to 18

Question 19

Which of the following graphical tools is not used to study the shapes of distributions?

a) histogram
b) dot plot
c) stem-and-leaf display
d) scatter plot

Answer 19

d) scatter plot

Scatter plots are used to display the relationship between two variables.

Question 20

Students in Professor Smith’s business statistics course have evaluated the overall effectiveness of the professor’s instruction on a five-point scale, where a score of 1 indicates very poor performance and a score of 5 indicates outstanding performance. The raw scores are displayed in the accompanying table:

1 4 4 5 5 3 4 3 4 1
5 5 4 4 2 3 3 2 3 3
4 5 5 5 5 3 2 3 3 2

What is the relative frequency of the students who gave Professor Smith an evaluation of 3?

a) 0.5
b) 15
c) 9
d) 0.3

Answer 20

d) 0.3

Nine of the 30 students gave Professor Smith a 3. The relative frequency is thus 9/30 = 0.3.

Question 21

A city in California spent $6 million repairing damage to its public buildings in Year 1. The following table shows the categories where the money was directed.

Cause Percent
Termites 22%
Water Damage 6 %
Mold 12 %
Earthquake 27 %
Other 33 %

How much more did the city spend to fix damage caused by termites compared to the damage caused by water?

a) $360,000
b) $720,000
c) $1,320,000
d) $960,000

Answer 21

d) 960 000

The city spent 22% on termite damage and 6% on water damage. The difference is 16%. The total dollar value spent on the difference is 16% of $6 million—that is, $6,000,000 × 0.16 = $960,000.

Question 22

The following data represent scores on a pop quiz in a statistics section.

45 66 74 72 62 44 55 70 33 82
56 56 84 16 16 47 32 32 17 37

Suppose the data are grouped into five classes, and one of them will be “30 up to 44” —that is, {x; 30 ≤ x < 44}. The relative frequency of this class is _____.

a) 0.25
b) 4
c) 5
d) 0.20

Answer 22

d) 0.20

There are four data values that are at least 30 but less than 44. They are 32, 32, 33, and 37. So the relative frequency is 4/20 = 0.20.

Question 23

The following frequency distribution shows the frequency of the asking price, in thousands of dollars, for current homes on the market in a particular city.

Asking Price Frequency
$350 up to $400 12
$400 up to $450 9
$450 up to $500 17
$500 up to $550 11
$550 up to $600 6

What percentage of houses has an asking price between $350,000 and under $400,000?

a) 16.4%
b) 21.8%
c) 30.9%
d) 33.3%

Answer 23

b) 21.8

For quantitative data, a relative frequency distribution identifies the proportion of observations that falls into each class: class relative frequency is equal to the class frequency divided by total number of observations. 12 / (12 + 9 + 17 + 11 + 6) = 12 / 55 = 21.8%

Question 24

A company collected the ages from a random sample of its middle managers, with the resulting frequency distribution shown below.

Class
Interval Frequency
20 to< 25 8
25 to< 30 6
30 to< 35 5
35 to< 40 12
40 to< 45 15
45 to< 50 7

What is the relative frequency for the class with the greatest frequency?

a) .226
b) .288
c) .132
d) .231
e) .283

Answer 24

e) .283

Measurements = 53; largest interval has 15 measurements.15/53 = .283.

Question 25

The Statistical Abstract of the United States provided the following frequency distribution of the number of people who live below the poverty level by region.

Region Number of People (in 1000s)
Northeast 6,166
Midwest 7,237
South 15,501
West 8,372

What is the percentage of people who live below the poverty level in the West or Midwest?

a) 41.87%
b) 31.96%
c) 35.96%
d) 41.58%

Answer 25

a) 41.87%

The percent frequency is the percent of observations in a category (or categories), and it equals the frequency divided by the total number of observations and multiplied by 100. (7237 + 8372) / 37276 = 41.87%

Question 26

Consider the following data on distances traveled by people to visit the local amusement park and calculate the relative frequency for the distances over 24 miles.

Distance Frequency
1-8 miles 15
9-16 miles 12
17-24 miles 7
25-32 miles 5
33-40 miles 1

a) .375
b) .125
c) .025
d) .150
e) .325

Answer 26

d) .150

(5 + 1) = 6 over 24 miles; 6/40 = .15.