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Chapter 4
Describing Data: Displaying and Exploring Data
True/False
1. A dot plot and a scatter diagram are different names for the same graph.
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2. A dot plot is an easy way to represent the relationship between two variables.
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3. A dot plot is useful for quickly graphing frequencies in a small data set.
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4. A stem and leaf diagram shows the actual data values.
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5. There is some loss of information when raw data is tallied into a stem-and-leaf display.
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6. For a stem-and-leaf display, the leaf for the value 98 is 9.
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7. The stem in a stem-and-leaf display is the leading digit.
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8. In a stem-and-leaf display, the leaf represents a class of a frequency distribution.
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9. In a stem-and-leaf display, the leaf represents a member of a class in a frequency distribution.
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10. In a stem-and-leaf display, for each class, the leaves are arranged or sorted from smallest to largest.
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11. In a stem-and-leaf display, it is easy to find the range for a data set.
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12. Quartiles divide a distribution into four equal parts.
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13. A percentile divides a distribution into one hundred equal parts.
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14. A student scored in the 85th percentile on a standardized test. This means that the student scored
lower than 85% of all students who took the test.
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15. Quartiles are another way to describe the central location of a distribution.
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16. Quartiles are another way to describe the dispersion of a distribution.
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17. The 50th percentile of a distribution is the same as the distribution mean.
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18. A percentile can be a decile, but a decile can not be a quartile.
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19. A quartile can be a decile, but a decile can not be a percentile.
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20. For a distribution, the 2nd quartile, the 5th decile, and the 50th percentile, are the same as the median.
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21. The interquartile range is the difference between the values of the first and third quartile, indicating
the range of the middle fifty percent of the observations.
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22. A box plot graphically shows data that are in percentiles.
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Test Bank, Chapter 4
23. The "box" in a box plot shows the interquartile range.
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24. An outlier is a data point that occurs in the first quartile.
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25. An outlier is a value in a data set that is inconsistent with the rest of the data.
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26. A box plot shows the relative symmetry of a distribution.
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27. A box plot shows a distribution's mean and mode.
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28. A box plot shows the range of values that correspond to the upper 25% of the distribution.
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29. In a box plot, if a value is more than 1.5 times the standard deviation from the first or third quartile,
the value is an outlier.
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30. In a box plot, if a value is more than 1.5 times the interquartile range from the first or third quartile,
the value is an outlier.
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31. The coefficient of variation is a measure of relative dispersion that expresses the standard deviation
as a percent of the mean.
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32. The Pearson's coefficient of skewness is a measure of distribution's symmetry.
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33. The coefficient of variation is useful for comparing distributions with different units.
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34. The coefficient of variation is computed by dividing the standard deviation by the median and
multiplying the quotient by 100.
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35. Negatively skewed indicates that a distribution is not symmetrical. The long tail is to the left or in the
negative direction.
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36. In a negatively skewed distribution, the mean is smaller than the median or mode and the mode
occurs at the peak of the curve.
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37. If Pearson's coefficient of skewness is equal to 0, then the mean and median are equal.
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38. If Pearson's coefficient of skewness is negative, then the mean is greater than the median.
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39. If Pearson's coefficient of skewness is negative, then the distribution is skewed to the left.
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40. If Pearson's coefficient of skewness is negative, then the distribution is skewed to the right.
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41. A scatter diagram of sales versus production may be constructed by plotting the data on a graph
labeled with sales on the Y-axis and production on the X-axis.
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42. A relationship between gender and preference for Coke or Pepsi can be best represented by a scatter
diagram.
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43. A relationship between gender and preference for Coke or Pepsi can be best represented by a
contingency table.
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Test Bank, Chapter 4
Multiple Choice
44. A dot plot shows
A) The general shape of a distribution
B) The mean, median, and mode
C) The relationship between two variables
D) The interquartile range.
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45. A row of a stem-and-leaf chart appears as follows: 3 | 0 1 3 5 7 9. Assume that the data is rounded to
the nearest unit.
A) The frequency of the class is seven.
B) The minimum value in the class is 0.
C) The maximum value in the class is 39.
D) The class interval is 5.
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46. The test scores for a class of 147 students are computed. What is the location of the test score
associated with the third quartile?
A) 111
B) 37
C) 74
D) 75%
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47. What statistics are needed to draw a box plot?
A) Minimum, maximum, median, first and third quartiles
B) Median, mean and standard deviation
C) A median and an interquartile range
D) A mean and a standard deviation.
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48. A box plot shows
A) The mean and variance
B) The relative symmetry of a distribution for a set of data
C) The percentiles of a distribution
D) The deciles of a distribution
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49. What does the interquartile range describe?
A) The lower 50% of the observations
B) The middle 50% of the observations
C) The upper 50% of the observations
D) The lower 25% and the upper 25% of the observations
E) None of the above
Answer
50. The coefficient of variation for a set of annual incomes is 18%; the coefficient of variation for the
length of service with the company is 29%. What does this indicate?
A) More dispersion in the distribution of the incomes compared with the dispersion of their length of
service
B) More dispersion in the lengths of service compared with incomes
C) Dispersion in the two distributions (income and service) cannot be compared using percents
D) Dispersions are equal
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51. Mr. and Mrs. Jones live in a neighborhood where the mean family income is $45,000 with a standard
deviation of $9,000. Mr. and Mrs. Smith live in a neighborhood where the mean is $100,000 and the
standard deviation is $30,000. What is the relative dispersion of the family incomes in the two
neighborhoods?
A) Jones 40%, Smith 20%
B) Jones 20%, Smith 30%
C) Jones 30%, Smith 20%
D) Jones 50%, Smith 33%
E) None of the above
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52. A large oil company is studying the number of gallons of gasoline purchased per customer at selfservice pumps. The mean number of gallons is 10.0 with a standard deviation of 3.0 gallons. The median
is 10.75 gallons. What is the Pearson's coefficient of skewness?
A) -1.00
B) -0.75
C) +0.75
D) +1.00
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53. What is the value of the Pearson coefficient of skewness for a distribution with a mean of 17, median
of 12 and standard deviation of 6?
A) +2.5
B) -2.5
C) +0.83
D) -0.83
Answer:
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Test Bank, Chapter 4
54. A study of business faculty at state supported institutions in Ohio revealed that the arithmetic mean
salary for nine months is $52,000 and a standard deviation of $3,000. The study also showed that the
faculty had been employed an average (arithmetic mean) of 15 years with a standard deviation of 4 years.
How does the relative dispersion in the distribution of salaries compare with that of the lengths of
service?
A) Salaries about 100%, service about 50%
B) Salaries about 6%, service about 27%
C) Salaries about 42%, service about 81%
D) Salaries about 2%, service about 6%
Answer
55. What is the possible range of values for the coefficient of variation?
A) -1 and +1
B) -3 and +3
C) 0% and 100%
D) Unlimited values
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56. A research analyst wants to compare the dispersion in the price-to-earnings ratios for a group of
common stocks with their return on investment (ROI). For the price-to-earnings ratios, the mean is 10.9
and the standard deviation is 1.8. The mean return on investment is 25 percent and the standard deviation
5.2 percent. What is the relative dispersion for the price-to-earnings ratios and return on investment?
A) Price-to-earnings = 32.0 percent, ROI =19.0 percent
B) Price-to-earnings =16.5 percent, ROI = 20.8 percent
C) Price-to-earnings =132.0 percent, ROI =190.0 percent
D) Price-to-earnings = 50.0 percent, ROI =10.0 percent
Answer
57. A study of the scores on an in-plant course in management principles and the years of service of the
employees enrolled in the course resulted in these statistics:
- Mean test score was 200 with a standard deviation of 40
- Mean number of years of service was 20 years with a standard deviation of 2 years.
In comparing the relative dispersion of the two distributions, what are the coefficients of variation?
A) Test 50%, service 60%
B) Test 100%, service 400%
C) Test 20%, service 10%
D) Test 35%, service 45%
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58. A large group of inductees was given a mechanical aptitude and a finger dexterity test. The
arithmetic mean score on the mechanical aptitude test was 200, with a standard deviation of 10. The
mean and standard deviation for the finger dexterity test were 30 and 6 respectively. What is the relative
dispersion in the two groups?
A) Mechanical aptitude 5 percent, finger dexterity 20 percent
B) Mechanical aptitude 20 percent, finger dexterity 10 percent
C) Mechanical aptitude 500 percent, finger dexterity 200 percent
D) Mechanical aptitude 50 percent, finger dexterity 200 percent
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59. A sample of experienced typists revealed that their mean typing speed is 87 words per minute and the
median is 73. The standard deviation is 16.9 words per minute. What is the Pearson's coefficient of
skewness?
A) -2.5
B) -4.2
C) +4.2
D) +2.5
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60. A study of the net sales of a sample of small corporations revealed that the mean net sales is $2.1
million, the median $2.4 million, the modal sales $2.6 million and the standard deviation of the
distribution is $500,000. What is the Pearson's coefficient of skewness?
A) -9.1
B) +6.3
C) -3.9
D) +2.4
E) None of the above
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61. In a scatter diagram, we describe the relationship between
A) two variables measured at the ordinal level
B) two variables, one measured as an ordinal variable and the other as a ratio variable
C) two variables measured at the interval or ratio level
D) a variable measure on the interval or ratio level and time.
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62. In a contingency table, we describe the relationship between
A) two variables measured at the ordinal or nominal level.
B) two variables, one measured as an ordinal variable and the other as a ratio variable
C) two variables measured at the interval or ratio level
D) a variable measure on the interval or ratio level and time.
Answer:
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Test Bank, Chapter 4
Fill-in-the-Blank
63. What chart or graph is useful for illustrating frequencies? _______________________.
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64. For a stem-and-leaf display, what is the stem for the value 67? ____.
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Essay
65. Construct a stem-and-leaf display for the following data:
29
33
46
22
69
32
57
35
30
19
37
21
54
38
58
34
65
26
39
42
38
35
55
31
50
22
52
59
20
51
Answer:
66. From the following stem-and-leaf display, find the minimum value, the 1st quartile, the median, the
3rd quartile, and the maximum value. List and interpret the interquartile range.
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Fill-in-the-Blank
67. For a stem-and-leaf display, what is the leaf for the value 123? ____.
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68. If you are constructing a stem-and-leaf display, the "3" in 19.3 would be the ____________.
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69. If you are constructing a stem-and-leaf display, the "20" in 20.5 would be the _____________.
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70. What is the best way to display the relationship between two variables measured on an interval or
ratio level?
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71. What is the main advantage of a stem-and-leaf chart over a histogram? ___________________
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72. The percentile range is the distance between any two _______________.
Answer: percentiles
Difficulty: Medium
Goal: 3
73. In a symmetric distribution, where is the 99th percentile located? _______________
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74. In a positively skewed distribution, where is the 99th percentile located? _______________
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75. In a negatively skewed distribution, where is the 1st percentile located? _______________
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76. If the mean of a distribution is smaller than the median and mode, what is the sign of Pearson's
coefficient of skewness? _______________
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77. A frequency distribution may be divided into how many percentiles? ___
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Test Bank, Chapter 4
78. For a set of data, how many quartiles are there? _____
Answer: three
Difficulty: Medium
Goal: 3
79. If two sets of data are measured in different units, what statistic can be used to compare their
dispersions? ___________________________________
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80. What unit of measurement is used to express the coefficient of variation? _________
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81. The coefficient of variation is a measure of _______________.
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82. The research director of a large oil company conducted a study of the buying habits of consumers
with respect to the amount of gasoline purchased at full-service pumps. The arithmetic mean amount is
11.5 gallons and the median amount is 11.95 gallons. The standard deviation of the sample is 4.5 gallons.
What is the Pearson's coefficient of skewness? ________
Answer:
83. Rainbow Trout, Inc. feeds fingerling trout in special ponds and markets them when they attain a
certain weight. A group of 9 trout (considered the population) were isolated in a pond and fed a special
food mixture called Grow Em Fast. At the end of the experimental period, the weights of the trout were
(in grams): 124, 125, 123, 120, 124, 127, 125, 126 and 121. Another special mixture, Fatso 1B, was used
in another pond. The mean of the population was computed to be 126.9 grams and the standard deviation
was 1.20 grams. Which food results in a more uniform weight? ____________
Answer:
84. The annual incomes of the five vice presidents of Elly's Industries are: $41,000, $38,000, $32,000,
$33,000 and $50,000. The annual incomes of Unique, another firm similar to Elly's Industries, were also
studied and found to have a mean of $38,900 and a standard deviation of $6,612. What company has the
greater coefficient of variation? ______________
Answer
85. The spread in the annual prices of stocks selling under $10 and those selling over $60 are to be
compared. The mean price of the stocks selling under $10 is $5.25 and the standard deviation is $1.52.
The mean price of those stocks selling over $60 is $92.50 and the standard deviation is $5.28. Why
should the coefficient of variation be used to compare the dispersion in the prices?
______________________
Answer:
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86. The lengths of stay on the cancer floor of Community Hospital were organized into a frequency
distribution. The mean length was 28 days, the median 25 days and the modal length 23 days. The
standard deviation was computed to be 4.2 days. What is the Pearson's coefficient of skewness?
__________
Answer:
87. A sample of the homes currently offered for sale revealed that the mean asking price is $75,900, the
median $70,100 and the modal price is $67,200. The standard deviation of the distribution is $5,900.
What is the Pearson's coefficient of skewness? __________
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88. The Pearson's coefficient of skewness (Sk) measures the amount of skewness and may range from 3.0 to +3.0. It is computed by subtracting the median from the mean, multiplying the result by 3 and
dividing by? ________________
Answer:
Essay
89. Given the sample information in the following table regarding public opinion on gun control, who is
more likely to favor gun control?
Party Affiliation
Democrat
Republican
Total
Favor
90
90
180
Opinion on Gun Control
Oppose
No opinion
98
46
54
10
152
56
Total
234
154
388
Answer:
Fill-in-the-Blank
Use the following to answer questions 90-94:
A telemarketing firm is monitoring the performance of its employees based on the number of sales per
hour. One employee had the following sales for the last 20 hours
9
4
5
4
2
7
6
8
5
4
6
4
4
5
4
5
4
4
7
8
90. What is the median for the distribution of number of sales per hour? ____________
Answer:
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Test Bank, Chapter 4
91. What is the first quartile for the distribution of number of sales per hour? ________________
Answer:
92. What is the third quartile for the distribution of number of sales per hour? _____________
Answer:
93. For the distribution of number of sales per hour, 50% are greater than ____________
Answer:
94. For the distribution of number of sales per hour, 50% of the observations are between __________
and ____________.
Answer:
Use the following to answer questions 95-101:
The following stem and leaf display reports the number of boat shipments per week by Ottertail Boats,
Inc.
11| 1 5 9
12| 0 1 2 2 6 9
13| 0 1 2 3 4 5 5 7 8 8 9
14| 2 6 8
15| 0 1 2 4 5 7 8 9
16| 1 5 7 9
95. How many weeks were included in the study?____________
Answer:
96. How many observations are in the third class?__________
Answer:
97. What are the smallest and largest values?___________
Answer:
98. List the actual values in the fourth class._______________
Answer:
99. How often did the company complete 111 shipments? ____________
Answer
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100. How often did the company complete more than 140 shipments? __________
Answer:
101. What is the median value? _______________
Answer:
Essay
102. What is the common purpose of a scatter diagram and a contingency table?
Answer:
103. What is the difference between a scatter diagram and a contingency table?
Answer: : 6,7
104. Draw a negatively or positively skewed distribution and show the relative locations of the mean,
median, and mode.
Answer:
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Test Bank, Chapter 4