Test Bank, Chapter 3
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Chapter 3
Describing Data: Numerical Measures
True/False
1. A value that is typical or representative of the data is referred to as a measure of central location.
Answer: True Difficulty: Easy Goal: 1
2. The arithmetic mean is the sum of the observations divided by the total number of observations.
Answer: True Difficulty: Easy Goal: 1
3. For a set of data arranged or sorted in numerical order, the value of the observation in the center is
called the weighted mean.
Answer: False Difficulty: Easy Goal: 1
4. A set of ordinal, interval or ratio level data may only have one mode.
Answer: False Difficulty: Easy Goal: 1
5. If a variable is measured at the interval or ratio level, all the values are included when computing the
mean.
Answer: True Difficulty: Easy Goal: 2 AACSB: EU
6. A variable measured at the interval or ratio level can have more than one arithmetic mean.
Answer: False Difficulty: Easy Goal: 2
7. The mode is the value of the observation that appears most frequently.
Answer: True Difficulty: Easy Goal: 1
8. A distribution that has the same shape on either side of the center is said to be symmetrical.
Answer: True Difficulty: Easy Goal: 3
9. A negatively skewed distribution is not symmetrical. The long tail is to the left or in the negative
direction.
Answer: True Difficulty: Easy Goal: 3
10. The geometric mean is the nth root of n observations.
Answer: True Difficulty: Medium Goal: 1
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11. A statistic is a measurable characteristic of the population.
Answer: False Difficulty: Easy Goal: 1
12. A parameter is a measurable characteristic of a sample.
Answer: False Difficulty: Easy Goal: 1
13. The median can be determined for any set of interval-level data.
Answer: True Difficulty: Easy Goal: 2
14. Extremely high or low scores affect the value of the median.
Answer: False Difficulty: Easy Goal: 2
15. The sum of the deviations from the mean for the set of numbers 4, 9 and 5 will equal zero.
Answer: True Difficulty: Easy Goal: 2
16. For salaries of $102,000, $98,000, $45,000, $106,000 and $101,000, the arithmetic mean would be an
appropriate average.
Answer: False Difficulty: Easy Goal: 2 AACSB: REF
17. Three persons earn $8 an hour, six earn $9 an hour, and one earns $12 an hour. The weighted mean
hourly wage is $9.
Answer: True Difficulty: Medium Goal: 1 AACSB: AS
18. For any distribution, there are an equal number of values above the mean and below it.
Answer: False Difficulty: Easy Goal: 2
19. For a data set with an even number of ungrouped values, the median is the arithmetic mean of the two
middle values.
Answer: True Difficulty: Easy Goal: 1
20. For a data set with an even number of ungrouped values, half of the values will be less than the
median.
Answer: True Difficulty: Easy Goal: 1
21. In a negatively skewed distribution, the mean is always greater than the median.
Answer: False Difficulty: Easy Goal: 3
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22. In a negatively skewed distribution, the mean is smaller than the median or mode and the mode
occurs at the peak of the curve.
Answer: True Difficulty: Easy Goal: 3
23. In a positively skewed distribution, the mode is greater than the median.
Answer: False Difficulty: Medium Goal: 3
24. Dispersion is the degree of variation in the data.
Answer: True Difficulty: Easy Goal: 4
25. The mean deviation is the mean of the actual values of the deviations from the arithmetic mean.
Answer: False Difficulty: Medium Goal: 4
26. The variance is the mean of the sum of the squared deviations between each observation and the
median.
Answer: False Difficulty: Medium Goal: 4
27. The standard deviation is the positive square root of the variance.
Answer: True Difficulty: Medium Goal: 4
28. Chebyshev’s Theorem gives the proportion of observations in any data set that occurs within k
standard deviations of the mean, where k is greater than 1.0.
Answer: True Difficulty: Medium Goal: 6
29. The Empirical states that about 68% of the observation will lie within one standard deviation of the
mean; about 95% of the observations will lie within two standard deviations of the mean; and virtually all
(99.7%) will lie within three standard deviations of the mean.
Answer: True Difficulty: Medium Goal: 6
30. The mean absolute deviation is the most widely used measure of dispersion.
Answer: False Difficulty: Easy Goal: 4
31. For a symmetrical distribution, the variance is equal to the standard deviation.
Answer: False Difficulty: Medium Goal: 4
32. In a company, the standard deviation of the ages of female employees is six years and the standard
deviation of the ages of male employees is ten years. These statistics indicate that there is more spread in
the ages of the female employees.
Answer: False Difficulty: Easy Goal: 4 AACSB: MD
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33. If we find the deviation of each value from the median, the sum of these deviations is always zero.
Answer: False Difficulty: Easy Goal: 4
34. If a frequency distribution is open-ended, the variance cannot be determined.
Answer: True Difficulty: Medium Goal: 4
35. The range cannot be computed for data grouped in a frequency distribution having an open end.
Answer: True Difficulty: Medium Goal: 4
Multiple Choice
36. For which measure of central location will the sum of the deviations of each value from the data’s
average will always be zero?
A) Mode
B) Mean
C) Median
D) Geometric mean
E) None of the above
Answer: B Difficulty: Easy Goal: 1
37. For a set of grouped or ungrouped data, which measures of central location always have only one
value?
A) Mode and median
B) Mode and mean
C) Mode and geometric mean
D) Mean and median
Answer: D Difficulty: Easy Goal: 2
38. Which measures of central location are not affected by extremely small or extremely large values?
A) Mean and median
B) Mean and mode
C) Mode and median
D) Geometric mean and mean
E) None of the above
Answer: C Difficulty: Easy Goal: 2
39. What is the relationship among the mean, median and mode in a symmetric distribution?
A) They are all equal
B) The mean is always the smallest value
C) The mean is always the largest value
D) The mode is the largest value
Answer: A Difficulty: Easy Goal: 3
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40. For a data set, half of the observations are always greater than the ________ .
A) Median
B) Mode
C) Mean
D) Geometric mean
Answer: A Difficulty: Easy Goal: 2 AACSB: REF
41. What is the lowest level of measurement that a median can be computed?
A) Nominal
B) Ordinal
C) Interval
D) Ratio
Answer: B Difficulty: Medium Goal: 2
42. For an ungrouped data set with an odd number of observations that have been sorted or arrayed from
smallest to largest values, where is the median located?
A) n
B) n/2
C) (n + 1)/2
D) n + 1/2
Answer: C Difficulty: Medium Goal: 1 AACSB: AS
43. Which measure of central location is used to determine an average annual percent increase?
A) Arithmetic mean
B) Weighted mean
C) Mode
D) Geometric mean
E) Median
Answer: D Difficulty: Easy Goal: 1
44. If a frequency distribution has open-ended intervals at the extremes, which measure of central
location is the most difficult to estimate?
A) Median
B) Mode
C) Mean
D) All of the above
E) None of the above
Answer: C Difficulty: Medium Goal: 2
45. Which one of the following is referred to as the population mean?
A) Statistic
B)
C) Sample
D) None of the above
Answer: B Difficulty: Medium Goal: 1
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46. Fifteen accounting majors had an average grade of 90 on a finance exam. Seven marketing majors
averaged 85, while ten finance majors averaged 93 on the same exam. What is the weighted mean for the
32 students taking the exam?
A) 89.84
B) 89.33
C) 89.48
D) Impossible to determine without more information
Answer: A Difficulty: Medium Goal: 1 AACSB: AS
47. In the calculation of the arithmetic mean for grouped data, which value is used to represent all the
values in a particular class?
A) The upper limit of the class
B) The lower limit of the class
C) The frequency of the class
D) The cumulative frequency preceding the class
E) The class midpoint.
Answer: E Difficulty: Medium Goal: 2
48. On a survey questionnaire, students were asked to indicate their class rank in college. If there were
only four choices from which to choose, which measure(s) of central location would be appropriate to use
for the data generated by that questionnaire item?
A) Mean and median
B) Mean and mode
C) Mode and median
D) Mode only
E) Median only
Answer: C Difficulty: Medium Goal: 1
49. What is the median of 26, 30, 24, 32, 32, 31, 27 and 29?
A) 32
B) 29
C) 30
D) 29.5
Answer: D Difficulty: Medium Goal: 1
50. The net incomes (in $ millions) of a sample of steel fabricators are: $86, $67, $86 and $85. What is
the modal net income?
A) $67
B) $85
C) $85.5
D) $86
Answer: D Difficulty: Easy Goal: 1
51. A sample of light trucks using diesel fuel revealed the following distribution based on fuel efficiency,
i.e., miles per gallon (mpg).
mpg Number of Trucks
10 up to 13 2
13 up to 16 5
16 up to 19 10
19 up to 22 8
22 up to 25 3
25 up to 28 2
What is the arithmetic mean miles per gallon?
A) 16.9
B) 18.6
C) 17.0
D) 17.9
E) None of the above
Answer: B Difficulty: Hard Goal: 1
52. The ages of newly hired, unskilled employees were grouped into the following distribution:
Ages
Number
18 up to 21
4
27 up to 30
