Exam Questions Descriptive Statistics Chapter 3 - Business Stats Contemporary Decision 10e | Test Bank by Ken Black by Ken Black. DOCX document preview.
File: ch03, Chapter 3: Descriptive Statistics
True/False
1. Statistical measures used to yield information about the center or the middle parts of a group of numbers are called the measures of central tendency.
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
2. The most appropriate measure of central tendency for nominal-level data is the median.
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
3. The most frequently occurring value in a set of data is called the mode.
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
4. An appropriate measure of central tendency for ordinal data is the mode.
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
5. It is inappropriate to use the mean to analyze data that are not at least interval level in measurement.
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
6. The lowest appropriate level of measurement for the median is ordinal.
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
7. The middle value in an ordered array of numbers is called the mode.
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
8. Average deviation is a common measure of the variability of data containing a set of numbers.
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
9. The sum of deviations about the arithmetic mean for a given set of data is always equal to zero.
Response: See section 3.2 Measures of Variability
Difficulty: Easy
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
10. The average of the squared deviations about the arithmetic mean is called the variance.
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
11. The sample standard deviation is calculated by taking the square root of the population standard deviation.
Response: See section 3.2 Measures of Variability
Difficulty: Easy
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
12. The coefficient of variation is unitless.
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
13. Skewness and kurtosis of a data set are measures of the shape of the distribution.
Response: See section 3.3 Measures of Shape
Difficulty: Easy
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots
14. A nonzero value of the skewness indicates asymmetry of the distribution of the data.
Response: See section 3.3 Measures of Shape
Difficulty: Easy
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots
15. If the mean, median, and mode are equal, then the distribution is positively skewed.
Response: See section 3.3 Measures of Shape
Difficulty: Easy
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots
16. If the mean of a distribution is greater than the median, then the distribution is positively skewed.
Response: See section 3.3 Measures of Shape
Difficulty: Medium
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots
17. If the median of a distribution is greater than mean, then the distribution is skewed to the left.
Response: See section 3.3 Measures of Shape
Difficulty: Medium
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots
18. A box and whisker plot is determined from the mean, the smallest and the largest values, and the lower and upper quartile.
Response: See section 3.3 Measures of Shape
Difficulty: Hard
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots
19. An outlier of a data set is determined from the lower and upper quartile
Response: See section 3.3 Measures of Shape
Difficulty: Medium
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots
20. A histogram can be used in business analytics to determine if a variable is approximately normally distributed.
Ans: True
Response: See section 3.4: Business Analytics Using Descriptive Statistics
Difficulty: Easy
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
21. A business analyst could use descriptive statistics of skewness to determine if the empirical rule could appropriately be applied to a variable.
Ans: False
Response: See section 3.4: Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
22. By comparing the mean and median of a variable in a large data set, a business analyst can assess the variability within the values of that variable.
Ans: False
Response: See section 3.4: Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
23. From a large data set, a variable would be considered positively skewed if the descriptive statistics showed the median to be less than the mean.
Ans: True
Response: See section 3.4: Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
24. If a large data set can be assumed to be normally distributed, then a business analyst could apply the normality rule to determine a range with approximately 60% of the data.
Ans: False
Response: See section 3.4: Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
25. In a large data set, an analyst finds that the interquartile range is 102 to 331, indicating that about 75% of the data points fall within that range.
Ans: False
Response: See section 3.4: Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
Multiple Choice
26. A statistics student made the following grades on 7 tests: 76, 82, 92, 95, 79, 86, and 92. What is the mean grade?
a) 78
b) 80
c) 86
d) 84
e) 88
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
27. A statistics student made the following grades on 7 tests: 76, 82, 92, 95, 79, 86, and 92. What is the median grade?
a) 86
b) 76
c) 82
d) 94
e) 95
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
28. A statistics student made the following grades on 7 tests: 76, 82, 92, 95, 79, 86, and 92. What is the mode?
a) 79
b) 82
c) 86
d) 92
e) 76
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
29. A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 34, 39, 41, 35, and 41. The mean time (in minutes) required for this trip was _______.
a) 35
b) 41
c) 37.5
d) 38
e) 35.5
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of ungrouped data.
30. A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 34, 39, 41, 35, and 41. The median time (in minutes) required for this trip was _______.
a) 39
b) 41
c) 37.5
d) 38
e) 35.5
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
31. A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 34, 39, 41, 35, and 41. The mode time required for this trip was _______.
a) 39
b) 41
c) 37.5
d) 38
e) 35
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
32. A sample was taken of the salaries of four employees from a large company. The following are their salaries (in thousands of dollars) for this year: 33, 36, 41, and 47. The median of their salaries is approximately _________.
a) 38.5
b) 34.5
c) 34
d) 44.5
e) 38
Response: See section 3.1 Measures of Central Tendency
Difficulty: Easy
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
33. A sample was taken of the salaries of four employees from a large company. The following are their salaries (in thousands of dollars) for this year: 33, 36, 41, and 47. The variance of their salaries is approximately
a) 28.19
b) 75.59
c) 37.58
d) 6.13
e) 5.31
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
34. The number of standard deviations that a value (x) is above or below the mean is the _________________.
a) absolute deviation
b) coefficient of variation
c) interquartile range
d) z score
e) correlation coefficient
Response: See section 3.2 Measures of Variability
Difficulty: Easy
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
35. The empirical rule says that approximately what percentage of the values would be within 2 standard deviations of the mean in a bell shaped set of data?
a) 95%
b) 68%
c) 50%
d) 97.7%
e) 100%
Response: See section 3.2 Measures of Variability
Difficulty: Easy
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
36. The empirical rule says that approximately what percentage of the values would be within 1 standard deviation of the mean in a bell shaped set of data?
a) 95%
b) 68%
c) 50%
d) 97.7%
e) 100%
Response: See section 3.2 Measures of Variability
Difficulty: Easy
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
37. According to Chebyshev's Theorem, approximately how many values in a large data set will be within 2 standard deviations of the mean?
a) At least 75%
b) At least 68%
c) At least 95%
d) At least 89%
e) At least 99%
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
38. According to Chebyshev's theorem how many values in a data set will be within 3 standard deviations of the mean?
a) At least 75%
b) At least 68%
c) At least 95%
d) At least 89%
e) At least 99%
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
39. A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 38, 33, 36, 47, and 41. What is the variance for these sample data?
a) 28.5
b) 11
c) 22.8
d) 5.34
e) 4.77
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
40. A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 38, 33, 36, 47, and 41. What is the standard deviation for these sample data?
a) 28.5
b) 11
c) 22.8
d) 5.34
e) 4.77
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
41. A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 44, 39, 41, 35, and 41. What is the standard deviation for these sample data?
a) 0
b) 11
c) 3.32
d) 2.97
e) 10.69
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
42. The mean life of a particular brand of light bulb is 1200 hours and the standard deviation is 50 hours. We can conclude that at least 75% of this brand of bulbs will last between _______.
a) 1100 and 1300 hours
b) 1150 and 1250 hours
c) 1050 and 1350 hours
d) 1000 and 1400 hours
e) 950 and 1450 hours
Response: See section 3.2 Measures of Variability
Difficulty: Hard
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
43. The mean life of a particular brand of light bulb is 1200 hours and the standard deviation is 50 hours. It can be concluded that at least 89% of this brand of bulbs will last between _______.
a) 1100 and 1300 hours
b) 1150 and 1250 hours
c) 1050 and 1350 hours
d) 1000 and 1400 hours
e) 950 and 1450 hours
Response: See section 3.2 Measures of Variability
Difficulty: Hard
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
44. The mean life of a particular brand of light bulb is 1200 hours and the standard deviation is 75 hours. Tests show that the life of the bulb is approximately normally distributed. It can be concluded that approximately 68% of the bulbs will last between _______.
a) 900 and 1100 hours
b) 950 and 1050 hours
c) 975 and 1475 hours
d) 1050 and 1350 hours
e) 1125 and 1275 hours
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
45. Jessica Salas, President of Salas Products, is reviewing the warranty policy for her company's new model of automobile batteries. Life tests performed on a sample of 100 batteries indicated: (1) an average life of 75 months, (2) a standard deviation of 5 months, and (3) a bell-shaped battery life distribution. Approximately 68% of the batteries will last between ________________.
a) 70 and 80 months
b) 60 and 90 months
c) 65 and 85 months
d) 55 and 95 months
e) 60 and 100 months
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
46. Jessica Salas, President of Salas Products, is reviewing the warranty policy for her company's new model of automobile batteries. Life tests performed on a sample of 100 batteries indicated: (1) an average life of 75 months, (2) a standard deviation of 5 months, and (3) a bell-shaped battery life distribution. Approximately 95% of the batteries will last between ________________.
a) 70 and 80 months
b) 60 and 90 months
c) 65 and 85 months
d) 55 and 95 months
e) 60 and 100 months
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, mean absolute deviation, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
47. Jessica Salas, President of Salas Products, is reviewing the warranty policy for her company's new model of automobile batteries. Life tests performed on a sample of 100 batteries indicated: (1) an average life of 75 months, (2) a standard deviation of 5 months, and (3) a bell shaped battery life distribution. Approximately 99.7% of the batteries will last between ________________.
a) 70 and 80 months
b) 60 and 90 months
c) 65 and 85 months
d) 55 and 95 months
e) 50 and 100 months
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
48. Jessica Salas, President of Salas Products, is reviewing the warranty policy for her company's new model of automobile batteries. Life tests performed on a sample of 100 batteries indicated: (1) an average life of 75 months, (2) a standard deviation of 5 months, and (3) a bell-shaped battery life distribution. What percentage of the batteries will fail within the first 65 months of use?
a) 0.5%
b) 1%
c) 2.5%
d) 5%
e) 7.5%
Response: See section 3.2 Measures of Variability
Difficulty: Hard
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
49. The average starting salary for graduates at a university is $33,000 with a standard deviation of $2,000. If a histogram of the data shows that it takes on a mound shape, the empirical rule says that approximately 95% of the graduates would have a starting salary between _______.
a) 29,000 and 37,000
b) 27,000 and 39,000
c) 25,000 and 41,000
d) 31,000 and 35,000
e) 21,000 and 39,000
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
50. The average starting salary for graduates at a university is $33,000 with a standard deviation of $2,000. If a histogram of the data shows that it takes on a mound shape, the empirical rule says that approximately 68% of the graduates would have a starting salary between _______.
a) 29,000 and 37,000
b) 27,000 and 39,000
c) 25,000 and 41,000
d) 31,000 and 35,000
e) 21,000 and 39,000
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
51. Liz Chapa manages a portfolio of 250 common stocks. Her staff compiled the following performance statistics for two new stocks.
Rate of Return | ||
Stock | Mean | Standard Deviation |
Salas Products, Inc. | 15% | 5% |
Hot Boards, Inc. | 20% | 5% |
The coefficient of variation for Salas Products, Inc. is __________.
a) 300%
b) 100%
c) 33%
d) 5%
e) 23%
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
52. Liz Chapa manages a portfolio of 250 common stocks. Her staff compiled the following performance statistics for two new stocks.
Rate of Return | ||
Stock | Mean | Standard Deviation |
Salas Products, Inc. | 15% | 5% |
Hot Boards, Inc. | 20% | 5% |
The coefficient of variation for Hot Boards, Inc. is __________.
a) 400%
b) 100%
c) 33%
d) 40%
e) 25%
Ans: e
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
53. If stock A has a coefficient of variation of 30% and stock B has a coefficient of variation of 35%. Based on this measure of risk, which stock would be considered riskier?
a) Stock A
b) The values are so close, they would be considered to have the same level of risk
c) Stock B
d) Risk cannot be measured by the coefficient of variation
e) There is not enough information to answer
Ans: c
Response: See section 3.2 Measures of Variability
Difficulty: Medium
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
54. The following box and whisker plot was constructed for the age of accounts receivable.
The box and whisker plot reveals that the accounts receivable ages are _______.
a) skewed to the left
b) skewed to the right
c) not skewed
d) normally distributed
e) symmetrical
Response: See section 3.3 Measures of Shape
Difficulty: Easy
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
55. The following box and whisker plot was constructed for the age of accounts receivable.
The box and whisker plot reveals that the accounts receivable ages are _______.
a) skewed to the left
b) skewed to the right
c) not skewed
d) normally distributed
e) symmetrical
Response: See section 3.3 Measures of Shape
Difficulty: Easy
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
56. The following frequency distribution was constructed for the wait times in the emergency room.
The frequency distribution reveals that the wait times in the emergency room are _______.
a) skewed to the left
b) skewed to the right
c) not skewed
d) normally distributed
e) symmetrical
Response: See section 3.3 Measures of Shape
Difficulty: Easy
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
57. The following frequency distribution was constructed for the wait times to check out at the grocery store.
The frequency distribution reveals that the wait times to check out at the grocery store are _______.
a) skewed to the left
b) skewed to the right
c) not skewed
d) normally distributed
e) symmetrical
Response: See section 3.3 Measures of Shape
Difficulty: Easy
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
58. Shaun Connor, Human Resources Manager for American Oil Terminals (AOT), is reviewing the operator training hours at AOT nationally. His staff compiled the following table of national statistics on operators training hours.
West Coast Region | East Coast Region | |
Mean | 32 | 38 |
Median | 32 | 32 |
Mode | 32 | 27 |
Standard Deviation | 8 | 7 |
What can Shaun conclude from these statistics?
a) The East Coast distribution is skewed to the left.
b) The East Coast distribution is skewed to the right.
c) The West Coast distribution is skewed to the left.
d) The West Coast distribution is skewed to the right.
e) Both distributions are symmetrical.
Response: See section 3.3 Measures of Shape
Difficulty: Medium
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
59. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB. His staff compiled the following table of regional statistics on teller training hours.
Southeast Region | Southwest Region | |
Mean | 20 | 28 |
Median | 20 | 20 |
Mode | 20 | 21 |
Standard Deviation | 5 | 7 |
What can David conclude from these statistics?
a) The Southeast distribution is symmetrical.
b) The Southwest distribution is skewed to the left.
c) The Southeast distribution has the greater dispersion.
d) The Southeast distribution is skewed to the left.
e) The two distributions are symmetrical.
Response: See section 3.3 Measures of Shape
Difficulty: Easy
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
. Karen Merlott, VP for Strategic Planning at a recruitment firm, recently conduct a survey to determine customer satisfaction with job placement. She distributed the survey to 45 of the most recently placed executives. Two items on survey them to rate the importance of “initial interview process” and “satisfaction of final job placement” on a scale of 1 to 10 (with 1 meaning “not important” and 10 meaning “highly important”). Her staff assembled the following statistics on these two items.
Initial Interview Process | Satisfaction of Final Job Placement | |
Mean | 8.5 | 7.5 |
Median | 9 | 8.5 |
Mode | 9.0 | 9 |
Standard Deviation | 1.0 | 1.5 |
What can Karen conclude from these statistics?
a) The Initial Interview Process distribution is positively skewed.
b) The Initial Interview Process distribution is not skewed.
c) The Satisfaction of Final Job Placement distribution is negatively skewed.
d) The Satisfaction of Final Job Placement distribution is positively skewed.
e) Both are symmetrically distributed.
Response: See section 3.3 Measures of Shape
Difficulty: Medium
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
61. In its Industry Norms and Key Business Ratios, Dun & Bradstreet reported that Q1, Q2, and Q3 for 2,037 gasoline service stations' sales to inventory ratios were 20.8, 33.4, and 53.8, respectively. From this we can conclude that ____________.
a) 68% of these service stations had sales to inventory ratios of 20.8 or less
b) 50% of these service stations had sales to inventory ratios of 33.4 or less
c) 50% of these service stations had sales to inventory ratios of 53.8 or more
d) 95% of these service stations had sales to inventory ratios of 33.4 or more
e) 99% of these service stations had sales to inventory ratios of 53.8 or more
Response: See section 3.3 Measures of Shape
Difficulty: Easy
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
62. David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB. His staff report several statistics for teller training hours. The mean is 20 hours, the standard deviation is 5 hours, the median is 15 hours, and mode is 10 hours. The Pearsonian coefficient of skewness—or Pearson’s second skewness coefficient, defined as (3 × (μ – median)/σ)—for teller training hours is __________.
a) 6
b) 1
c) 3
d) 4
e) 0
Response: See section 3.3 Measures of Shape
Difficulty: Hard
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
63. A sample of 117 records of the selling price of homes from Feb 15 to Apr 30, 2018 was taken from the files maintained by the Albuquerque Board of Realtors. The following are summary statistics for the selling prices.
Variable | N | Mean | Minimum | Q1 | Median | Q3 | Maximum |
Prices | 117 | 106270 | 54000 | 77650 | 96000 | 121750 | 215000 |
From this we can conclude that,
a) There are no outliers
b) More homes were sold for greater than $121750 than for less than $77650
c) 68% of the selling price of these homes is from $77650 to $121750
d) 25% of the selling price of these homes is at least $121750
e) The distribution of selling price of these homes is negatively skewed.
Response: See section 3.3 Measures of Shape
Difficulty: Hard
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
64. A company is reviewing the database of customer purchases over the past 3 years. Using descriptive statistics on this large data set, a business analyst found the following values.
Variable | Count | Mean | Minimum | Q1 | Median | Q3 | Maximum |
Purchases | 56,472 | 105.21 | 10.24 | 31.09 | 74.88 | 117.23 | 201.40 |
From this we can conclude that,
a) 95% of these purchases are between $105.24 and $74.88
b) The distribution of these purchases is negatively skewed
c) More of these purchases had values less than $74.88 than above that amount
d) The distribution of these purchases is positively skewed
e) The distribution of these purchases is not skewed
Ans: d
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
65. A company is reviewing the database of customer purchases over the past 3 years. Using descriptive statistics on this large data set, a business analyst found the following values.
Variable | Count | Mean | Minimum | Q1 | Median | Q3 | Maximum |
Purchases | 56,472 | 105.21 | 10.24 | 31.09 | 74.88 | 117.23 | 201.40 |
From this we can conclude that,
a) 68% of these purchases are between $105.24 and $74.88
b) The distribution of these purchases is negatively skewed
c) 50% of these purchases are between $31.04 and $117.23
d) 50% of these purchases are less than $105.24
e) The distribution of these purchases is not skewed
Ans: c
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
66. A company is reviewing the database of customer purchases over the past 3 years. Using descriptive statistics on this large data set, a business analyst found the following values.
Variable | Count | Mean | Minimum | Q1 | Median | Q3 | Maximum |
Purchases | 56,472 | 105.21 | 10.24 | 31.09 | 74.88 | 117.23 | 201.40 |
From this we can conclude that,
a) 68% of these purchases are between $105.24 and $74.88
b) The distribution of these purchases is negatively skewed
c) 50% of these purchases are between $105.21 and $117.23
d) 50% of these purchases are less than $105.24
e) More of these purchases were below the mean than above the mean
Ans: e
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
67. After obtaining a large data set, a business analyst will first want to determine _________.
a) descriptive statistics of all variables
b) the standard deviation of key variables
c) only the mean of all variables
d) what other variables should be included in the data set
e) when the updated version of the data set will be available
Ans: a
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
68. A business analyst is considering a data set reflecting the number of products purchased at one time, there is a minimum of 45 and a maximum of 61. Given that the data set the number of products purchased for 5,791 purchases, the number of values at the mode would be expected to be ________.
a) less than 45
b) a large number since there is little variation in the number of products purchased
c) a small number since there is little variation in the number of products purchased
d) greater than 61
e) greater than 5,791
Ans: b
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
69. A business analyst is considering a data set reflecting the number of products purchased at one time, there is a minimum of 45 and a maximum of 61. Given that the data set the number of products purchased for 5,791 purchases, the range would be ________.
a) less than 45
b) 53
c) 5791
d) greater than 61
e) 16
Ans: e
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
70. A business analyst is considering a data set reflecting the number of products purchased at one time, there is a mean of 159 and a standard deviation of 43.2. Given that the data set the number of products purchased for 5,791 purchases and is mound shaped, the analyst would expect 68% of the data points to be ________.
a) between 115.8 and 202.2
b) less than 5,791
c) between 72.6 and 245.4
d) greater than 61
e) between 43.2 and 159
Ans: a
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
71. A statistics student has a mean score of 92 in the first 3 tests. Suppose there are a total of 4 tests and all of them have equal weight. You can also assume that there is no extra credit in the last test. What is the best possible final average this student can get?
a) 96
b) 95
c) 94
d) 93
e) there is not enough information to find out
Response: See section 3.1 Measures of Central Tendency
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
72. A statistics student made the following grades on the first 6 tests: 76, 82, 92, 95, 79, 86. The total number of tests for the semester is 7. What could be her median score for the whole semester?
a) It’s not possible to answer without knowing the score on the last test.
b) 76
c) 82
d) 92
e) 95
Response: See section 3.1 Measures of Central Tendency
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
73. A statistics student made the following grades on the first 6 tests: 76, 82, 92, 95, 92, 86. The total number of tests for the semester is 7. If the median score for the whole semester was 92, what could not have been the score of the last test?
a) 77
b) 92
c) 93
d) 94
e) 96
Response: See section 3.1 Measures of Central Tendency
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
74. Your company is testing a new auto engine in a race car. The race car is on a 2-mile track. If the first lap was exactly at 2 minutes, so that the average speed for the first lap was 1.00 mile per minute, what would be the time required for the second lap so that the overall average speed will be 4 miles per minute?
a) It’s not possible to end up with an overall average speed of 4 miles per minute.
b) 1.0 minute
c) 0.8 minutes
d) 0.6 minutes
e) 0.4 minutes
Response: See section 3.1 Measures of Central Tendency
Difficulty: Hard
AACSB: Analysis
Bloom’s level: Application
Learning Objective: 3.1: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.
75. The mean life of a particular brand of light bulb is 1200 hours. If you know that at about 95% of this brand of bulbs will last between 1100 and 1300 hours, then what is the standard deviation of the light bulbs’ life?
a) 25
b) 50
c) 75
d) 100
e) 200
Response: See section 3.2 Measures of Variability
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
76. The mean life of a specialized essential electronic component in one of your company’s main products is 80 months, and its standard deviation is 6 months. It is known that the life for this component is not normally distributed. We can conclude that at least 96% of these components will last between _______.
a) 74 and 86 months
b) 68 and 92 months
c) 66 and 94 months
d) 64 and 96 months
e) 50 and 110 months
Response: See section 3.2 Measures of Variability
Difficulty: Hard
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
77. An electrical component for one of the main products your company produces is specified to have an electrical impedance of 2.15 ohms. However, the manufacturing process is not perfect and there is some variation on the actual impedance of these components. A recent statistical study indicated that in fact, the impedances are normally distributed with a mean impedance of 2.15 ohms and a standard deviation of 0.05 ohms. When the impedance exceeds 2.25 ohms, the product malfunctions so that component must be rejected and replaced by one whose impedance is within the acceptable limit. If you need 1350 usable components, how many components should you order?
a) 1608
b) 1422
c) 1421
d) 1417
e) 1384
Response: See section 3.2 Measures of Variability
Difficulty: Hard
AACSB: Analytic
Bloom’s level: Application
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
78. You have computed the z score for a value. Then you realize that the actual standard deviation of the population is 25% larger than the one you used for computing the z value. Your corrected z value will be _______.
a) 25% smaller than the original value
b) 25% larger than the original value
c) 75% smaller than the original value
d) 20% larger than the original value
e) 20% smaller than the original value
Response: See section 3.2 Measures of Variability
Difficulty: Hard
AACSB: Analytic
Bloom’s level: Application
Learning Objective: 3.2: Apply various measures of variability—including the range, interquartile range, variance, and standard deviation (using the empirical rule and Chebyshev’s theorem)—to a set of data.
79. A box-and-whisker plot for last year’s data is compared with a box-and-whisker plot for this year’s data. The biggest change is that the median is moved from the left side of the box to the right side of the box. The other elements of the plot remained fairly constant. Based on this change, it can be concluded that ___________.
a) the data have become more positively skewed
b) the data are less skewed than in the previous year
c) the skew has not changed between the two years
d) the data have become more negatively skewed
e) the data are more skewed than in the previous year
Ans: d
Response: See section 3.3 Measures of Shape
Difficulty: Medium
AACSB: Analytic
Bloom’s level: Application
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
80. If a data set is negatively skewed, which calculations cannot be used?
a) Business analytics
b) Chebyshev’s theorem
c) Descriptive statistics
d) Measures of variance
e) Empirical rule
Ans: e
Response: See section 3.3 Measures of Shape
Difficulty: Hard
AACSB: Analytic
Bloom’s level: Application
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
81. Pearson’s second skewness coefficient is defined as (3 × (μ – median)/σ). You are examining financial statistics for the rate of return of a financial product your company sells and find out that the standard deviation is 0.5 and the Pearson coefficient of skewness is 1.5. Suppose that by the end of this year, you receive the updated statistics and find out that the mean increased by 0.2 and the median and standard deviation stayed unchanged. What would be the updated value of Pearson’s second skewness coefficient?
a) 0.4
b) 1.2
c) 2.5
d) 2.6
e) 2.7
Response: See section 3.3 Measures of Shape
Difficulty: Hard
AACSB: Analytic
Bloom’s level: Application
Learning Objective: 3.3: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.
82. A business analyst compares 2017 daily sales to 2018 daily sales using descriptive statistics for each. In 2017, the standard deviation of daily sales was 73.87, while in 2018 the standard deviation of daily sales was 136.32. The analyst could conclude that ____________.
a) in 2018 there was more variation in daily sales
b) the average daily sales increased between those two years
c) in 2018 there was less variation in daily sales
d) the variance remained the same between the two years
e) the average daily sales decreased between those two years
Ans: a
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
AACSB: Analytic
Bloom’s level: Application
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
83. Considering sales levels at each hour of operation in a shoe store, a business analyst finds that the mode is between 3pm and 4pm each day. The analyst could conclude that ___________.
a) half of shoe sales occur before 3pm
b) hourly sales of shoes are normally distributed
c) half of shoe sales occur after 4pm
d) 3pm to 4pm has more shoe sales than other hours
e) 3pm to 4pm is when any retail business would have the most sales
Ans: d
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
AACSB: Analytic
Bloom’s level: Application
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
84. Considering sales levels at each hour of operation in a shoe store over the past year, a business analyst looks at a histogram that has the selling hours of the day along the horizontal axis and the frequency of sales along the vertical axis. The analyst notices that the distribution is left skewed. From this, the analyst could conclude that ___________
a) most sales are made later in the day
b) sales are made evenly throughout the day
c) the store should close earlier in the day due to lack of sales at that time
d) most sales are made earlier in the day
e) most sales are made in the middle of the day
Ans: e
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
85. The hourly production of a plastic cup company is tracked over several months and is found to be normally distributed. Given a mean of 15,630 cups and a standard deviation of 251 cups, about what percent of all hours of production should produce between 15,379 and 15,881 cups?
a) 50%
b) 68%
c) 75%
d) 95%
e) nearly 100%
Ans: b
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
86. The hourly production of a plastic cup company is tracked over several months and is found to be normally distributed. Given a mean of 15,630 cups and a standard deviation of 251 cups, about what percent of all hours of production should produce between 15,128 and 16,132 cups?
a) 50%
b) 68%
c) 75%
d) 95%
e) nearly 100%
Ans: d
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
87. The hourly production of a plastic cup company is tracked over the most recent several months and is found to be normally distributed. Comparing the mean of this data set to a similar data set collected last year during the same months, the business analyst notices that the mean has increased, while the overall shape of the distribution has not. Which of the following would not be a possible explanation for this difference?
a) the overall distribution has shifted to the right
b) one or two large outliers occurred in the more recent data set
c) the mode increased as well
d) one or two small outliers occurred in the earlier data set
e) the overall distribution has shifted to the left
Ans: e
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
88. The hourly production of a plastic cup company is tracked over several months and is found to be normally distributed. A business analyst creates a box and whisker plot from those data and finds that the box starts at 15259 to 16,001. Based on the graph, what percentage of the hourly sales would the analyst expect to find within that range?
a) 50%
b) 68%
c) 75%
d) 95%
e) nearly 100%
Ans: a
Response: See section 3.4 Business Analytics Using Descriptive Statistics
Difficulty: Medium
Learning Objective: 3.4: Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid businesspeople in making better decisions.
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Business Stats Contemporary Decision 10e | Test Bank by Ken Black
By Ken Black