Download Chapter 3 - Data Description – Study Guide

Chapter 3 - Data Description – Study Guide
1. What is the term for a characteristic or measure obtained by using all the data values for
a specific population?
A) variable B) mode C) statistic D) parameter
2. Which of the following is the correct mean for the given data?
7, 8, 13, 9, 10, 11
A) 10 B) 9.7 C) 9.67 D) 9
3. Which of the following is the mode for the given data?
5, 4, 3, 4, 5, 6, 5, 5, 3, 4
A) 3 B) 4 C) 5 D) 6
4. Find the mode for the number of police officers in selected city districts.
24, 26, 24, 30, 23, 28, 19, 31, 24, 26, 19
A) 23 B) 24 C) 26 D) 28
5. The following data set could also be referred to as a data array.
3, 4, 2, 7
6. A weighted mean is used when the values of the data set are not all equally represented.
7. What is the mean of the following numbers?
1, 3, 6, 8, 12
A) 3 B) 5 C) 6 D) 7
8. What is the median of the following numbers?
3, 5, 8, 10, 14
A) 5 B) 7 C) 8 D) 9
9. What is the median of the following numbers?
–12, –9, –5, –4, 0
A) –6 B) –5 C) –4 D) –2
10. What is the midrange of the following numbers?
7, 13, 12, 14, 6, 14, 20, 20, 20
A) 13 B) 14 C) 7 D) 20
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Chapter 3 - Data Description
11. The median of {–1, 6, 3, 2, –1} is
12. The mean of {6, 13, 11, 9, 11} is
13. Find the median for the following data.
6, 7, 4, 5, 3, 7, 4
A) 3 B) 4 C) 5 D) 7
14. In a unimodal, symmetrical distribution as shown in the figure below.
A)
B)
C)
D)
The mean is the same as the median, but the mode can be different.
The mean, the median, and the mode are the same.
The median and the mode are the same, but the mean can be different.
The mean, the median, and the mode are different.
15. The median can be a more appropriate measure of central tendency if the distribution of
the data is extremely skewed.
16. If a distribution is negatively skewed as shown in the figure below, the mean will fall to
the right of the median and the mode will be on the left of the median.
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Chapter 3 - Data Description
17. For the sample 1, 8, 7, 2, 9, 15, and 18, the mean is 7.6.
18. A ______________ is the midpoint in a data array.
19. The ________________ is the mode for grouped data.
20. Find the mean, mode, median, and midrange value for the following data set.
12, 15, 18, 18, 15, 22, 15, 30, 12
21. What is the mean of the following numbers?
–13, –10, –6, –5, –1
A) –10 B) –7 C) –6 D) –3
22. What is the median of the following numbers?
–13, 1, –1, –5, –1, –6, –5, –1
A) –7 B) –3 C) –5 D) –1
23. What is the mode of the following numbers?
–12, 2, 0, –4, 0, –2, –5
A) –6 B) –2 C) –4 D) 0
24. The median of {–5, –3, –3, –3, –5, 1} is
25. The mean of {–3, –1, –1, –1, –3, 3} is
26. Find the weighted mean for three exams if the first one was worth 75 points and the
student received a score of 70%, the second was worth 50 points and the student
received a score of 80% and the third was worth 30 points and the student received a
score of 95%?
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Chapter 3 - Data Description
27. A student received the following grades: An A in Statistics (4 credits), a B in Physics II
(5 credits), a B in Sociology (3 credits), a B in a Literature seminar (2 credits), and a D
in Tennis (1 credit). Assuming A = 4 grade points, B = 3 grade points, C = 2 grade
points, D = 1 grade point, and F = 0 grade points, the student's grade point average is:
A) 3.00 B) 3.47 C) 3.24 D) 3.12
28. Determine the range for this data: 4, 7, 3, 16, 5, 22, and 8.
A) 4 B) 3 C) 14 D) 19
29. Determine the range for this data: 7, 15, 11, 9, 23
A) 7 B) 11 C) 16 D) 23
30. What is the range of the numbers –5, 1, –7, 2, 10
A) –5 B) 1 C) 3 D) 17
31. The range of the set of numbers {6, 13, 3, 10, 5} is
A) 3 B) 13 C) 8 D) 10
32. The maximum of the set of numbers {6, 15, -5, 11, 5} is
A) -5 B) 15 C) 9 D) 12
33. The minimum of the set of numbers {–2, 16, -5, 11, 5} is
A) –2 B) 16 C) 9.5 D) 18
34. Given that the variance for a data set is 1.20, what would be the standard deviation?
A) 1.10 B) 1.44 C) 1.20 D) 0.60
35. Given that the mean of a set of data is 25 and the standard deviation is 3, what would be
the coefficient of variation?
A) 0.12 B) 12% C) 8.33 D) 833%
36. The variance is the square root of the standard deviation of a set of data.
37. The range of a data set is the distance between the highest value and the lowest value.
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Chapter 3 - Data Description
38. Chebyshev's theorem can be used to find the minimum percentage of data values that
will fall between any two given values.
39. The coefficient of variation is the mean divided by the standard deviation expressed as a
percentage.
40. The _______________and ______________ are used to determine the consistency of a
variable.
41. _______________ applies to any distribution regardless of its shape.
42. If a set of data has 49 points and variance 36, then the standard deviation is
A) 5.14 B) 0.12 C) 0.86 D) 6.00
43. If a set of 9 numbers has standard deviation 10, then it's variance is
A) 100.00 B) 3.33 C) 33.33 D) 30.00
44. The range of the dataset {–5, –9, 0, 11, –2} is
45. The grades for a trigonometry exam follow. Find the range.
85, 76, 93, 82, 84, 90, 75
A) 76 B) 9 C) 11 D) 18
46. A normal distribution in which approximately 68% of the data values fall within one
standard deviation of the mean behaves according to
A) the empirical rule.
C) a boxplot.
B) a symmetrical distribution.
D) differential statistics.
47. The unbiased estimator is included in the formula for calculating the variance of a
sample because without it, the computed variance usually underestimates the population
variance.
48. The ______________ is the average of the squares of the distance each value is from
the mean.
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Chapter 3 - Data Description
49. If a sample of data has mean 12 and variance 25, then it's coefficient of variation is
50. For a set of data with mean 30 and variance 16, approximaely 68% of the values will
fall between 22 to 38.
51. According to Chebyshev's theorem, the proportion of values from a data set that is
further than 2 standard deviations from the mean is:
A) 0.50 B) 0.13 C) 1.00 D) 0.25
52. In the figure below, what class boundary has 30% of the data?
A) 0.5–20.5 B) 20.5–40.5 C) 40.5–60.5 D) 60.5–80.5
Ans: C Difficulty: Easy Objective: 3 Section: 4 Similar Exercise: 3-4-16
53. The interquartile range or IQR is found by subtracting the mean from the maximum
value of a data set.
54. The percentile corresponding to a given value X is computed by adding the 0.5 to
number of values below X and dividing this value by the total number of values within
the data set.
55. ______________ divide the distribution into four groups, and __________divide the
distribution into ten groups.
56. ______________ are either extremely high or extremely low data values compared with
the rest of the data.
Ans: Outliers
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Chapter 3 - Data Description
57. If a student scored 86 points on a test where the mean score was 80 and the standard
deviation was 3. The student's z-score was
A) 26.67 B) 28.67 C) 0.67 D) 2.00
58. Find the z score for each student and indicate which one is higher.
s5
Art Major
X  50
X  46
Theater Major X  70
X  75
s7
A) The art major has a higher score than the theater major.
B) The theater major has a higher score than the art major.
C) Both students have the same score.
D) Neither student received a positive score; therefore, the higher score cannot be
determined.
59. What is the correct standard score for a batter who normally averages 0.325, with a
standard deviation of 0.065 if he scores 0.410 for one game?
A) 1.308 B) 0.410 C) 0.325 D) 1.275
60. Which of the following is true?
A) D5  P5  Q5 B) D50  P5  Q25
C) D5  P50  Q2
D) D50  P5  Q2
61. For the table below, calculate the cumulative percent of the students that fell within the
B class.
Grade
Class Boundaries
Frequency
A
89.5–99.5
4
B
79.5–89.5
7
C
69.5–79.5
11
D
59.5–69.5
3
F
49.5–59.5
3
A) 14% B) 25% C) 11% D) 39%
62. If a student scored 70 points on a test where the mean score was 78 and the standard
deviation was 6. The student's z-score was
A) 13.00 B) 0.22 C) –0.22 D) –1.33
63. If the value 7 has z-score of –1 in a dataset, then the mean of that dataset is
A) 7 B) 6 C) 8 D) It cannot be determined from the data given
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Chapter 3 - Data Description
64. If the mean of a set of data is 20.00, and 26.00 has a z-score of 0.75, then the standard
deviation must be:
A) 8.00 B) 64.00 C) 4.00 D) 32.00
65. Given the following data set, find the value that corresponds to the 75th percentile.
10, 44, 15, 23, 14, 18, 72, 56
Ans: 50
Difficulty: Hard Objective: 3 Section: 4 Similar Exercise: 3-4-19
66. If the mean of a set of data is 24.00, and 18.40 has a z-score of –1.40, then the standard
deviation must be:
A) 4.00 B) 16.00 C) 2.00 D) 8.00
67. A stem and leaf plot is a data plot that uses part of a data value as the stem and part of
the data value as the leaf to form groups or classes.
68. Methods commonly called traditional statistics include using measures of position,
Chebyshev's theorem, and the coefficient of variation.
69. All the values in a dataset are between 6 and 15, except for one value of 85. That value
85 is likely to be
A) the range B) an outlier C) the mean D) the boxplot
70. Choose the correct statement describing the following stem and leaf plot for grades on a
linear algebra exam.
A)
B)
C)
D)
The range of the grades is between 23 and 98.
Of the 29 students who took the exam, nine scored between 80 and 89.
There are no gaps in the data.
The data is bimodal.
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Chapter 3 - Data Description
71. Find Q1 , Q2 , and Q3 for the following data set.
7, 21, 32, 38.
Q1  14 , Q2  26.5 , and Q3  35
A)
C)
Q1  10 , Q2  25 , and Q3  36
B)
D)
Q1  5
, Q2  20 , and Q3  39
Q1  14 , Q2  25 , and Q3  25
72. Given the following boxplot where m is the median value, what statement could be
made about the distribution of the data?
A)
The distribution is approximately symmetric.
B)
The distribution is positively skewed.
C)
The distribution is negatively skewed.
D)
No statement can be made about the data because no data values are shown on the
plot.
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Chapter 3 - Data Description
73. A five-number summary of a data set consists of the minimum, Q1 , the mean, Q3 , and
the maximum.
74. In exploratory data analysis, ______________ are used instead of quartiles to construct
boxplots.
75. Make a boxplot for the following data set.
24, 15, 34, 92, 67, 34, 78, 45, 53, 67, 83, 46
76. If the boxplot for one set of data is much wider than the boxplot for a second set of data,
then
A) the mean of the first set of data must be larger than the mean of the second set of
data
B) the median of the first set of data must be larger than the median of the second set
of data
C) the second set of data must contain several outliers
D) none of the above need to be true
77. If the five number summary for a set of data is –2, 1, 4, 5, and 14, then the mean of this
set of data is
A) 6 B) 4 C) 3 D) there is insufficient information to calculate the mean
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