Deck 3: Graphical Descriptive Techniques II

Question 1

According to the stem-and-leaf plot below,the median quiz score for this data set is 8.
$$\begin{array} { l } \text { Stem-and-leaf of Quiz Score; } \mathrm { N } = 75 \\\text { Leaf Unit = } 1 \\\end{array}$$
$\begin{array}{c}\begin{array}{l}9 \\14 \\21 \\26 \\33 \\(8) \\34 \\27 \\19 \\10 \end{array}\begin{array}{l}0 \\0 \\1 \\1 \\2 \\2 \\3 \\3 \\4 \\4 \end{array}\begin{array}{l}000112333 \\56899 \\0000123 \\66699 \\3334445 \\66677888 \\0023344 \\56669999 \\000122233 \\5556667799 \end{array}\end{array}$

Answer 1

False

Question 2

According to the stem-and-leaf plot below,this data set has a negative median.
$$\begin{array}{l}\text { Stem-and-leaf of P/E ratio; } N = 75\\\begin{array} { l r l } \text { Leaf Unit } = \text { 0.01 } \\1 & - 2 & 6 \\2 & - 2 & 0 \\5 & - 1 & 555 \\8 & - 1 & 420 \\22 & - 0 & 9999988777665 \\36 & - 0 & 443221111111000 \\( 14 ) & 0 & 01122233333344 \\25 & 0 & 6667889999 \\14 & 1 & 0022222334 \\4 & 1 & 56 \\2 & 2 & 03\end{array}\end{array}$$

Answer 2

False

Question 3

The advantage of a stem-and-leaf display over a histogram is that we can see the actual observations.

Answer 3

True

Question 4

A relative frequency distribution describes the proportion of data values that fall within each category.

Question 5

The sum of cumulative relative frequencies always equals 1.

Question 6

A skewed histogram is one with a long tail extending either to the right or left.

Question 7

The intervals (classes)in a histogram do not overlap.

Question 8

The number of class intervals in a histogram depends on the number of observations in the data set.

Question 9

A stem-and-leaf display represents nominal data.

Question 10

According to the stem-and-leaf plot below,this data set is symmetric.
Stem-and-leaf of P/E ratio; $N = 10$
Loef Unit $= 0.10$

$\begin{array}{c}\begin{array}{lll}2\\4 \\(2) \\4 \\3 \\2 \\1\end{array}\begin{array}{r}-1 \\-0 \\-0 \\0 \\0 \\1 \\1\end{array}\begin{array}{l}53 \\97 \\65 \\3\\6\\3\\8 \end{array}\end{array}$

Question 11

A cumulative relative frequency distribution lists the number of observations that lie below each of the class limits.

Question 12

The sum of relative frequencies in a distribution always equals 1.

Question 13

The number of observations within each class may be found in a frequency distribution.

Question 14

When a distribution has more values to the right and tails to the left,we say it is skewed negatively.

Question 15

When a distribution has more values to the left and tails off to the right,it is skewed negatively.

Question 16

A histogram represents interval data.

Question 17

The intervals (classes)in a histogram are equally wide.

Question 18

A stem-and-leaf display reveals more information about the original data than does a histogram.

Question 19

In a histogram,each observation is assigned to one or more classes.

Question 20

A histogram is said to be symmetric if,when we draw a vertical line down the center of the histogram the two sides are nearly identical.

Question 21

Which of the following statements about histograms is false?

A) The intervals of a histogram do not overlap.
B) Every observation is assigned to one and only one class in a histogram.
C) The intervals of a histogram are equally wide.
D) None of these choices.

Question 22

The sum of the relative frequencies for all classes in a histogram always equals

A) the number of classes.
B) the class width.
C) the total of all the frequencies.
D) one.

Question 23

The relative frequency of a class in a histogram is computed by

A) dividing the frequency of the class by the number of classes.
B) dividing the frequency of the class by the class width.
C) dividing the frequency of the class by the total of all frequencies.
D) None of these choices.

Question 24

Compare the spread of the two histograms below.Which of the following is true?

A) Data Set A has a larger spread than Data Set B.
B) Data Set A has a smaller spread than Data Set B.
C) Data Set A has the same spread as Data Set B.
D) You cannot compare the spreads of these histograms without the original data.

Question 25

A modal class in a histogram is the class that includes

A) the largest number of observations.
B) the smallest number of observations.
C) the largest observation in the data set.
D) the smallest observation in the data set.

Question 26

Compare the two histograms below.Which statement is true?

A) The spread of histogram A is smaller than the spread of histogram B.
B) The spread of histogram A is larger than the spread of histogram B.
C) The spread of histogram A is the same as the spread of histogram B.
D) You cannot compare the spreads of these two histograms without the original data.

Question 27

Which of the following describes an ogive?

A) A graphical representation of frequencies.
B) A graphical representation of relative frequencies.
C) A graphical representation of cumulative frequencies.
D) A graphical representation of cumulative relative frequencies.

Question 28

Which of the following is true about a stem-and-leaf display?

A) You can recreate the original data set from it.
B) Its shape resembles a histogram turned on its side.
C) It provides an organized way to depict interval data.
D) All of these choices are true.

Question 29

Which of the following describes the shape of the histogram below?

A) Positively skewed
B) Negatively skewed
C) Symmetric
D) None of these choices

Question 30

A modal class is the class with the largest number of observations.

Question 31

Compare the two histograms below.Which statement is true?

A) The center of histogram A is lower than the center of histogram B.
B) The center of histogram A is higher than the center of histogram B.
C) The center of histogram A is the same as the center of histogram B.
D) You cannot compare the centers of these two histograms without the original data.

Question 32

Which of the following represents a graphical presentation of interval data?

A) A bar chart.
B) A histogram.
C) A pie chart.
D) All of these choices are true.

Question 33

Which of the following statements about histograms is true?

A) A histogram is a summary of interval data.
B) A histogram is made of a series of intervals,called classes.
C) The classes in a histogram cover the complete range of observations.
D) All of these choices are true.

Question 34

Experience shows that few students hand in their statistics exams early;most prefer to hand them in near the end of the test period.This means the time taken by students to write exams is positively skewed.

Question 35

Which of the following statements about shapes of histograms is true?

A) A histogram is said to be symmetric if,when we draw a vertical line down the center of the histogram,the two sides are identical in shape and size.
B) A negatively skewed histogram is one with a long tail extending to the left.
C) A positively skewed histogram is one with a long tail extending to the right.
D) All of these choices are true.

Question 36

Compare the two histograms below.Which statement is true?

A) The shape of histogram A is the same as the shape of histogram B.
B) The shape of histogram A is positively skewed compared to histogram B.
C) The shape of histogram A is negatively skewed compared to histogram B.
D) You cannot compare the shapes of these two histograms without the original data.

Question 37

The original observations cannot be determined once they are grouped into a frequency distribution.

Question 38

What does the length of each line of a stem-and-leaf display represent?

A) The percentage of observations in the interval represented by that stem.
B) The number of observations in the interval represented by that stem.
C) The total frequency of observations within or below that stem.
D) The number of digits to the left of the decimal point.

Question 39

The graph below is an example of a histogram.

Question 40

What values are displayed on a cumulative relative frequency distribution?

A) The number of observations that fall into each class interval.
B) The proportion of observations that fall into each class interval.
C) The number of observations that fall below each class interval.
D) The proportion of observations that fall below each class interval.

Question 41

Thirty voters participating in a recent election exit poll in Alabama were asked to state their political party affiliation.Coding the data 1 for Republican,2 for Democrat,and 3 for Independent,the data collected were as follows: 3,1,2,3,1,3,3,2,1,3,3,2,1,1,3,2,3,1,3,2,3,2,1,1,3,1,2,2,1,and 3.Develop a frequency distribution and a relative frequency distribution for this data.What does the data suggest about the strength of the political parties in Alabama?

Question 42

In a histogram a(n)____________________ class is the one with the largest number of observations.

Question 43

The largest value of a cumulative relative frequency is ____________________.

Question 44

We determine the approximate width of the classes by subtracting the smallest observation from the largest and dividing the answer by the number of ____________________.

Question 45

Teachers Ages
The ages (in years)of a sample of 25 teachers are as follows:

{Teachers Ages Narrative} Draw a stem-and-leaf display of this data.What is the minimum and maximum age of the teachers in this data set?

Question 46

We create a frequency distribution for interval data by counting the number of observations that fall into each of a series of intervals,called ____________________.

Question 47

A graph of the frequency distribution for interval data is called a(n)____________________.

Question 48

A(n)____________________ is a table that sorts data into class intervals (categories)and gives the number of observations in each interval (category).

Question 49

A(n)____________________ display shows the actual observations as well as the number of observations in each class.

Question 50

It is typical that when taking an exam,few students hand in their exams early;most prefer to reread their papers and hand them in near the end of the scheduled exam period.Under this scenario,a histogram of exam taking times is ____________________ skewed.

Question 51

The histogram below has a shape that is ____________________.

Question 52

A(n)____________________ histogram is one with a long tail extending to either the right or the left.

Question 53

A(n)____________________ is a graphical representation of the cumulative relative frequencies.

Question 54

Teachers Ages
The ages (in years)of a sample of 25 teachers are as follows:

{Teachers Ages Narrative} Draw a frequency histogram of this data which contains six classes.What is the shape of the histogram?

Question 55

The more observations we have,the ____________________ the number of class intervals we need to use to draw a useful histogram.

Question 56

For what type of data is a histogram appropriate?

Question 57

The length of each line in a step-and-leaf display represents the ____________________ of that class interval defined by the stems.

Question 58

Teachers Ages
The ages (in years)of a sample of 25 teachers are as follows:

{Teachers Ages Narrative} Draw a frequency histogram of this data which contains four classes.What is the shape of the histogram?

Question 59

A(n)____________________ histogram has two peaks,not necessarily equal in height.

Question 60

A histogram is said to be ____________________ if,when we draw a vertical line down the center of the histogram,the two sides are identical in shape and size.

Question 61

Electronics Company
At a meeting of regional offices managers of a national electronics company,a survey was taken to determine the number of employees the regional managers supervise in the operation of their departments.The results of the survey are shown below.

{Electronics Company Narrative} What proportion of managers supervise 3 employees?

Question 62

Internet Classes
A survey of 25 students was conducted to determine how they rate the quality of Internet classes.Students were asked to rate the overall quality from 0 (no quality at all)to 100 (extremely good quality).The stem-and-leaf display of the data is shown below.

{Internet Classes Narrative} What percentage of the students rated the overall quality of Internet classes as being 60 or below?

Question 63

Insurance Company
A representative from a local insurance agency selected a random sample of insured homeowners and recorded the number of claims made in the last three years,with the following results:

{Insurance Company Narrative} What number of claims was made by the highest proportion of homeowners?

Question 64

Test scores
The scores on a calculus test for a random sample of 40 students are as follows:

A supermarket's monthly sales (in thousands of dollars)for the last year were as follows:
Construct a relative frequency bar chart for this data set.How many observations are there in this data set?

Question 65

Insurance Company
A representative from a local insurance agency selected a random sample of insured homeowners and recorded the number of claims made in the last three years,with the following results:

{Insurance Company Narrative} How many homeowners are represented in the sample?

Question 66

Insurance Company
A representative from a local insurance agency selected a random sample of insured homeowners and recorded the number of claims made in the last three years,with the following results:
$$\begin{array} { | c | c | c | c | c | c | c | } \hline \text { Number of claims } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Frequency } & 9 & 20 & 14 & 13 & 5 & 3 \\\hline\end{array}$$

-{Insurance Company Narrative} How many total claims are represented in the sample?

Question 67

Test scores
The scores on a calculus test for a random sample of 40 students are as follows:

{Test Grades Narrative} Describe the distribution of exam scores.

Question 68

Test scores
The scores on a calculus test for a random sample of 40 students are as follows:
$$\begin{array} { l l l l l l l l l l } 63 & 74 & 42 & 65 & 51 & 54 & 36 & 56 & 68 & 57 \\62 & 64 & 76 & 67 & 79 & 61 & 81 & 77 & 59 & 38 \\84 & 68 & 71 & 94 & 71 & 86 & 69 & 75 & 91 & 55 \\48 & 82 & 83 & 54 & 79 & 62 & 68 & 58 & 41 & 47\end{array}$$

-The weights of a sample of 25 workers are given (in pounds): 164,148,137,157,173,156,177,172,169,165,145,168,163,162,174,152,156,168,154,151,174,146,134,140,and 171.Construct an ogive for the data.What proportion of the worker's weights are between 160 and 180 pounds;below 150 pounds;and at or above 140 pounds,respectively?

Question 69

Internet Classes
A survey of 25 students was conducted to determine how they rate the quality of Internet classes.Students were asked to rate the overall quality from 0 (no quality at all)to 100 (extremely good quality).The stem-and-leaf display of the data is shown below.

{Internet Classes Narrative} What percentage of the students rated the overall quality of Internet classes as being 70 or above?

Question 70

Insurance Company
A representative from a local insurance agency selected a random sample of insured homeowners and recorded the number of claims made in the last three years,with the following results:

{Insurance Company Narrative} What proportion of homeowners had no claims in the last three years?

Question 71

Test scores
The scores on a calculus test for a random sample of 40 students are as follows:

{Test Grades Narrative} Construct frequency and relative frequency distributions for this data set using seven class intervals.Describe the shape of the data set.

Question 72

Electronics Company
At a meeting of regional offices managers of a national electronics company,a survey was taken to determine the number of employees the regional managers supervise in the operation of their departments.The results of the survey are shown below.

{Electronics Company Narrative} How many regional offices are represented in the survey results?

Question 73

Test scores
The scores on a calculus test for a random sample of 40 students are as follows:

{Test Grade Narrative} Construct a relative frequency histogram for this data set and discuss its shape.

Question 74

Test scores
The scores on a calculus test for a random sample of 40 students are as follows:
$$\begin{array} { l l l l l l l l l l } 63 & 74 & 42 & 65 & 51 & 54 & 36 & 56 & 68 & 57 \\62 & 64 & 76 & 67 & 79 & 61 & 81 & 77 & 59 & 38 \\84 & 68 & 71 & 94 & 71 & 86 & 69 & 75 & 91 & 55 \\48 & 82 & 83 & 54 & 79 & 62 & 68 & 58 & 41 & 47\end{array}$$

-{Test Grades Narrative} Construct a cumulative frequency and a cumulative relative frequency distribution for this data.What proportion of the exam scores are less than 60? What proportion of the exam scores are 70 or more?

Question 75

Test scores
The scores on a calculus test for a random sample of 40 students are as follows:

Fifty two truck buyers were asked to indicate the car dealer they believed offered the best overall service.The four choices were A,B,C,and D as shown below:
Construct a table showing the frequencies and relative frequencies for this data set.What proportion of car buyers rated dealer D as the best?

Question 76

Test scores
The scores on a calculus test for a random sample of 40 students are as follows:

{Test Grades Narrative} Construct a stem-and-leaf display for this data set.Describe the shape of the data.

Question 77

Test scores
The scores on a calculus test for a random sample of 40 students are as follows:
$$\begin{array} { l l l l l l l l l l } 63 & 74 & 42 & 65 & 51 & 54 & 36 & 56 & 68 & 57 \\62 & 64 & 76 & 67 & 79 & 61 & 81 & 77 & 59 & 38 \\84 & 68 & 71 & 94 & 71 & 86 & 69 & 75 & 91 & 55 \\48 & 82 & 83 & 54 & 79 & 62 & 68 & 58 & 41 & 47\end{array}$$

-{Test Grades Narrative)Construct an ogive for this data set.Use the ogive to estimate the proportion of exam scores that are between 80 and 90.

Question 78

Test scores
The scores on a calculus test for a random sample of 40 students are as follows:

Consider the following cumulative frequency distribution.
Fill in the frequencies for each class in the above table.

Question 79

Electronics Company
At a meeting of regional offices managers of a national electronics company,a survey was taken to determine the number of employees the regional managers supervise in the operation of their departments.The results of the survey are shown below.

{Electronics Company Narrative} What is the cumulative relative frequency corresponding to 4 employees?

Question 80

Electronics Company
At a meeting of regional offices managers of a national electronics company,a survey was taken to determine the number of employees the regional managers supervise in the operation of their departments.The results of the survey are shown below.
$$\begin{array} { | c | c | c | c | c | c | } \hline \text { Number of emplayees supervised } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Frequency } & 7 & 11 & 14 & \mathbf { 8 } & 10 \\\hline\end{array}$$

-{Electronics Company Narrative} Across all of the regional offices,how many total employees were supervised by those surveyed?