CHAPTER 3

DESCRIPTIVE STATISTICS

CHAPTER LEARNING OBJECTIVES

1. Apply various measures of central tendency—including the mean, median, and mode—to a set of data. Statistical descriptive measures include measures of central tendency, measures of variability, and measures of shape.

Measures of central tendency are useful in describing data because they communicate information about the more central portions of the data. The most common measures of central tendency are the three Ms: mode, median, and mean. In addition, percentiles and quartiles are measures of central tendency.

The mode is the most frequently occurring value in a set of data. If two values tie for the mode, the data are bimodal. Data sets can be multimodal. Among other things, the mode is used in business to determine sizes.

The median is the middle term in an ordered array of numbers containing an odd number of terms. For an array with an even number of terms, the median is the average of the two middle terms. The expression (n ₊ 1)/2 specifies the location of the median. A median is unaffected by the magnitude of extreme values. This characteristic makes the median a most useful and appropriate measure of location in reporting such things as income, age, and prices of houses.

The arithmetic mean is widely used and is usually what researchers are referring to when they use the word mean. The arithmetic mean is the average. The population mean and the sample mean are computed in the same way but are denoted by different symbols. The arithmetic mean is affected by every value and can be inordinately influenced by extreme values.

Percentiles divide a set of data into 100 groups, which means 99 percentiles are needed. Quartiles divide data into four groups. The three quartiles are Q1, which is the lower quartile; Q2, which is the middle quartile and equals the median; and Q3, which is the upper quartile.

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. Measures of variability are statistical tools used in combination with measures of central tendency to describe data. Measures of variability provide a description of data that measures of central tendency cannot give: information about the spread of the data values. These measures include the range, mean absolute deviation, variance, standard deviation, interquartile range, z scores, and coefficient of variation for ungrouped data.

One of the most elementary measures of variability is the range. It is the difference between the largest and smallest values. Although the range is easy to compute, it has limited usefulness. The interquartile range is the difference between the third and first quartiles. It equals the range of the middle 50% of the data.

The mean absolute deviation (MAD) is computed by averaging the absolute values of the deviations from the mean. The mean absolute deviation provides the magnitude of the average deviation but without specifying its direction. The mean absolute deviation has limited use in statistics, but is occasionally used in the field of forecasting as a measure of error.

Variance is widely used as a tool in statistics but is used little as a stand-alone measure of variability. The variance is the average of the squared deviations about the mean. The square root of the variance is the standard deviation. It is also a widely used tool in statistics and is used more oft en than the variance as a stand-alone measure. Note that the formulas for computing the variance and standard deviation for a population and for a sample are slightly different.

The standard deviation is best understood by examining its applications in determining where data are in relation to the mean. The empirical rule and Chebyshev’s theorem are statements about the proportions of data values that are within various numbers of standard deviations from the mean.

The empirical rule reveals the percentage of values that are within one, two, or three standard deviations of the mean for a set of data. The empirical rule applies only if the data are in a bell-shaped distribution. According to the empirical rule, approximately 68% of all values of a normal distribution are within plus or minus one standard deviation of the mean. Ninety-five percent of all values are within two standard deviations either side of the mean, and virtually all values are within three standard deviations of the mean.

Chebyshev’s theorem also delineates the proportion of values that are within a given number of standard deviations from the mean. However, it applies to any distribution. According to Chebyshev’s theorem, at least 1 – 1/k² values are within k standard deviations of the mean. The z score represents the number of standard deviations a value is from the mean for normally distributed data.

The coefficient of variation is the ratio of a standard deviation to its mean, given as a percentage. It is especially useful in comparing standard deviations or variances that represent data with different means.

3. Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots. Two measures of shape are skewness and kurtosis. Skewness is the lack of symmetry in a distribution. If a distribution is skewed, it is stretched in one direction or the other. The skewed part of a graph is its long, thin portion. One measure of skewness is the Pearsonian coefficient of skewness. Kurtosis is the degree of peakedness of a distribution. A tall, thin distribution is referred to as leptokurtic. A flat distribution is platykurtic, and a distribution with a more normal peakedness is said to be mesokurtic.

A box and whisker plot is a graphical depiction of a distribution. The plot is constructed by using the median, the lower quartile, and the upper quartile. Box and whisker plots are rather sophisticated and can yield information about skewness and outliers.

4. Use descriptive statistics as a business analytics tool to better understand meanings and relationships in data so as to aid business people in making better decisions.

Descriptive statistics presented are at the foundation of statistical techniques and numerical measures. These techniques can be used to gain a basic understanding of data in business and aid management in making a variety of business decisions.

TRUE-FALSE STATEMENTS

1. Statistical measures used to yield information about the centre or the middle parts of a group of numbers are called the measures of central tendency.

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Knowledge

AACSB: Analytic

2. The most appropriate measure of central tendency for nominal-level data is the median.

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Knowledge

AACSB: Analytic

3. The most frequently occurring value in a set of data is called the mode.

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Knowledge

AACSB: Analytic

4. An appropriate measure of central tendency for ordinal data is the mode.

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Knowledge

AACSB: Analytic

5. It is inappropriate to use the mean to analyze data that are not at least interval level in measurement.

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Knowledge

AACSB: Analytic

6. The lowest appropriate level of measurement for the median is ordinal.

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Knowledge

AACSB: Analytic

7. The middle value in an ordered array of numbers is called the mode.

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Knowledge

AACSB: Analytic

8. Data sets with more than one mode are referred to as bimodal

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Knowledge

AACSB: Analytic

9. Percentiles divide a group of data into 99 parts

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Knowledge

AACSB: Analytic

10. A student reviewed their final grade and in addition to seeing their final grade, their professor gave them their percentile score. If a student scores in the 92^nd percentile that means that 92% of the students’ scores are above this student score.

Difficulty: Medium

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Knowledge

AACSB: Analytic

11. The mean of Q₃ and Q₂ is the same as the median.

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Knowledge

AACSB: Analytic

12. Average deviation is a common measure of the variability of data containing a set of numbers.

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Knowledge

AACSB: Analytic

13. The sum of deviations about the arithmetic mean for a given set of data is always equal to zero.

Difficulty: Easy

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Knowledge

AACSB: Analytic

14. The sum of the average of the squared deviations about the arithmetic mean, divided by the sample size minus one is called the sample variance.

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Knowledge

AACSB: Analytic

15. The sample standard deviation is calculated by taking the square root of the population standard deviation.

Difficulty: Easy

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Knowledge

AACSB: Analytic

16. 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.

Blooms: Knowledge

AACSB: Analytic

17. The lower the coefficient of variation value the lower the variability and thereby lower risk.

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.

Blooms: Knowledge

AACSB: Analytic

18. The greater the coefficient of variation value the lower the variability and thereby lower risk.

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.

Blooms: Knowledge

AACSB: Analytic

19. Measures of variability include percentiles and quartiles.

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.

Blooms: Knowledge

AACSB: Analytic

20. The approximate percentage number of values that lie with a given number of standard deviations about the mean is known as Chebyshev’s theorem.

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.

Blooms: Knowledge

AACSB: Analytic

21. The empirical rule may only be applied when data are known to be normally distributed.

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.

Blooms: Knowledge

AACSB: Analytic

22. Chebyshev’s theorem may be successfully applied regardless of the shape of the data distribution.

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.

Blooms: Knowledge

AACSB: Analytic

23. A z score value between -1.00 and +1.00 represent approximately 68% of the values in a given data set.

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.

Blooms: Knowledge

AACSB: Analytic

24. Skewness and kurtosis of a data set are measures of the shape of the distribution.

Difficulty: Easy

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Knowledge

AACSB: Analytic

25. Skewness indicates that a data distribution is symmetrical or asymmetrical.

Difficulty: Easy

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Knowledge

AACSB: Analytic

26. A measure of how peaked the data is, is called kurtosis.

Difficulty: Easy

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Knowledge

AACSB: Analytic

27. 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

Blooms: Knowledge

AACSB: Analytic

28. If the mean of a distribution is greater than the median, then the distribution is positively skewed.

Difficulty: Medium

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Knowledge

AACSB: Analytic

29. If the median of a distribution is greater than mean, then the distribution is skewed to the left.

Difficulty: Medium

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Knowledge

AACSB: Analytic

30. A box and whisker plot is determined from the mean, the smallest and the largest values, and the lower and upper quartile.

Difficulty: Hard

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Knowledge

AACSB: Analytic

31. 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

Blooms: Knowledge

AACSB: Analytic

32. A histogram can be used in business analytics to determine if a variable is approximately normally distributed.

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.

Blooms: Knowledge

AACSB: Analytic

33. A business analyst could use descriptive statistics of skewness to determine if the empirical rule could appropriately be applied to a variable.

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.

Blooms: Knowledge

AACSB: Analytic

34. 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.

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.

Blooms: Knowledge

AACSB: Analytic

35. 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.

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.

Blooms: Knowledge

AACSB: Analytic

36. 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.

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.

Blooms: Comprehension

AACSB: Analytic

37. 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.

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.

Blooms: Comprehension

AACSB: Analytic

MULTIPLE CHOICE QUESTIONS

38. A statistics student made the following grades on 5 tests: 84, 78, 88, 78, and 72. What is the mean grade?

a) 78

b) 80

c) 72

d) 84

e) 88

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

39. A statistics student made the following grades on 5 tests: 84, 78, 88, 72, and 72. What is the median grade?

a) 88

b) 72

c) 78

d) 80

e) 82

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

40. A statistics student made the following grades on 5 tests: 84, 78, 88, 78, and 82. What is the mode?

a) 78

b) 80

c) 88

d) 84

e) 82

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

41. A commuter travels many kilometres 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

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

42. A commuter travels many kilometres 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

Difficulty: Easy

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

43. A commuter travels many kilometres 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 modal time required for this trip was ___.

a) 39

b) 41

c) 37.5

d) 38

e) 35

Difficulty: Medium

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

44. The following measurements represent the gain or loss in the daily closing price of a security for ten consecutive days:
-1, 3, 4, 1, 0, -4, -3, 2, -1, 1
The mean gain or (loss) was _____

a) 0.20

b) 0.22

c) 2.00

d) 3.22

e) 5.80

Difficulty: Hard

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

45. The following measurements represent the gain or loss in the daily closing price of a security for ten consecutive days:
-1, 3, 4, 1, 0, -4, -3, 2, -1, 1
The median gain or (loss) was _____

a) -0.50

b) 0

c) 0.20

d) 0.50

e) 2.00

Difficulty: Hard

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

46. The following measurements represent the gain or loss in the daily closing price of a security for ten consecutive days:
-1, 3, 4, 1, 0, -4, -3, 2, -1, 1
The modal gain or (loss) was _____

a) -1

b) -1 and 1

c) -1, 1 and 3

d) 1 and 3

e) -1, 1 and 4

Difficulty: Hard

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

47. The following twelve data values are provided:

The 30^th percentile is _____

a) 187

b) 244

c) 250

d) 302

e) 578

Difficulty: Hard

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

48. The following twelve data values are provided:

The 80^th percentile is _____

a) 187

b) 244

c) 302

d) 440

e) 578

Difficulty: Hard

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

49. The following ten data values are provided:

The 80^th percentile is _____

a) 984

b) 995

c) 1609

d) 2346

e) 3083

Difficulty: Hard

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

50. The following ten data values are provided:

The value of Q₁ is _____

a) 973

b) 984

c) 995

d) 1609

e) 3083

Difficulty: Hard

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

51. The following twelve data values are provided:

The value of Q₃ is _____

a) 7739

b) 7596

c) 6188

d) 6032

e) 5352

Difficulty: Hard

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

52. The following twelve data values are provided:

The value of Q₁ is _____

a) 184.5

b) 187

c) 215.5

d) 440

e) 578

Difficulty: Hard

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

53. The following twelve sample data values, with a mean value of 337, are provided:

The sample standard deviation is _____

a) 17.58

b) 174.67

c) 182.44

d) 1070.12

e) 1117.70

Difficulty: Hard

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

54. The following twelve sample data values, with a mean value of 337, are provided:

The sample variance is _____

a) 308.92

b) 30511.33

c) 33285.00

d) 1145154.08

e) 1249259.00

Difficulty: Hard

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

55. The following twelve sample data values, with a mean value of 337, are provided:

The mean absolute deviation (MAD) is _____

a) 0.00

b) 144.17

c) 157.27

d) 308.92

e) Cannot be answered with the information provided

Difficulty: Hard

Learning Objective: Apply various measures of central tendency—including the mean, median, and mode—to a set of data.

Section Reference: 3.1 Measures of Central Tendency

Blooms: Application

AACSB: Analytic

56. 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.

Blooms: Application

AACSB: Analytic

57. 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

Difficulty: Easy

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Knowledge

AACSB: Analytic

58. The empirical rule says that approximately what percentage of the values would be within two standard deviations of the mean in a bell shaped set of data?

a) 95%

b) 68%

c) 50%

d) 97.7%

e) 100%

Difficulty: Easy

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Knowledge

AACSB: Analytic

59. The empirical rule says that approximately what percentage of the values would be within one standard deviation of the mean in a bell shaped set of data?

a) 95%

b) 68%

c) 50%

d) 97.7%

e) 100%

Difficulty: Easy

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Knowledge

AACSB: Analytic

60. According to Chebyshev's Theorem, how many values in a data set will be within two 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%

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Knowledge

AACSB: Analytic

61. According to Chebyshev's Theorem, how many values in a data set will be within three 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%

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Knowledge

AACSB: Analytic

62. A commuter travels many kilometres 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. The mean time required for this trip was 40 minutes. What is the variance for this sample data?

a) 8.8

b) 11

c) 0

d) 3

e) -2

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

63. A commuter travels many kilometres 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. The mean time required for this trip was 40 minutes. What is the standard deviation for this sample data?

a) 3.32

b) 2.97

c) 1.73

d) 11

e) -1.4

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

64. A commuter travels many kilometres 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. The mean time required for this trip was 40 minutes. What is the mean absolute deviation for this sample data?

a) 0

b) 12

c) 3

d) 2.4

e) 1.2

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

65. The mean life of a particular brand of light bulb is 1000 hours and the standard deviation is 50 hours. We can conclude that at least 75% of this brand of bulbs will last between ___.

a) 900 and 1100 hours

b) 950 and 1050 hours

c) 850 and 1150 hours

d) 800 and 1200 hours

e) 1050 and 1250 hours

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

66. The mean life of a particular brand of light bulb is 1000 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) 900 and 1100 hours

b) 950 and 1050 hours

c) 850 and 1150 hours

d) 800 and 1200 hours

e) 1050 and 1250 hours

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

67. The mean life of a particular brand of light bulb is 1000 hours and the standard deviation is 50 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) 850 and 1150 hours

d) 800 and 1200 hours

e) 1050 and 1250 hours

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

68. 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

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

69. 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

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

70. 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

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

71. 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%

Difficulty: Hard

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

72. The average starting salary for graduates at a university is $25,000 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) $23,000 and $27,000

b) $21,000 and $29,000

c) $19,000 and $31,000

d) $24,000 and $26,000

e) $26,000 and $28,000

Difficulty: Hard

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

73. The average starting salary for graduates at a university is $25,000 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) $23,000 and $27,000

b) $21,000 and $29,000

c) $19,000 and $31,000

d) $24,000 and $26,000

e) $26,000 and $28,000

Difficulty: Hard

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

74. Liz Chapa manages a portfolio of 250 common stocks. Her staff compiled the following performance statistics for two new stocks:

The coefficient of variation for Salas Products, Inc. is ___.

a) 300%

b) 100%

c) 33%

d) 5%

e) 23%

Difficulty: Medium

Learning Objective: 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.

Section Reference: 3.2 Measures of Variability

Blooms: Application

AACSB: Analytic

75. Liz Chapa manages a portfolio of 250 common stocks. Her staff compiled the following performance statistics for two new stocks.

The coefficient of variation for Hot Boards, Inc. is __________.

a) 400%

b) 100%

c) 33%

d) 40%

e) 25%

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.

Blooms: Application

AACSB: Analytic

76. 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

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.

Blooms: Comprehension

AACSB: Analytic

77. A given set of normally distributed data values has a mean of 335.40 and a standard deviation of 17.95. What is the z score for a value of 295.75?

a) 2.21

b) -2.21

c) 1.49

d) -1.49

e) There is not enough information to answer

Response: See section 3.2 Measures of Variability

Difficulty: Esy

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.

Blooms: Application

AACSB: Analytic

78. A given set of normally distributed data values has a mean of 75, a standard deviation of 8.50 and a z-score of 2.45. What is the approximate value of x₁?

a) 20.82

b) 51.00

c) 54.18

d) 95.85

e) 83.82

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.

Blooms: Application

AACSB: Analytic

79. A given set of normally distributed data values has a mean of 75, a standard deviation of 8.50 and a z-score of -2.45. What is the approximate value of x₁?

a) 20.82

b) 51.00

c) 54.18

d) 95.85

e) 83.82

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.

Blooms: Application

AACSB: Analytic

80. 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

Difficulty: Easy

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Knowledge

AACSB: Analytic

81. 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

Difficulty: Easy

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Knowledge

AACSB: Analytic

82. The following frequency distribution was constructed for the age of accounts receivable:

The frequency distribution 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

Difficulty: Easy

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Knowledge

AACSB: Analytic

83. The following frequency distribution was constructed for the age of accounts receivable:

The frequency distribution 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

Difficulty: Easy

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Knowledge

AACSB: Analytic

84. David Desreumaux, VP of Human Resources of Maritime Boat Manufacturing (MBM), is reviewing the employee training programs of MBM factories. His staff compiled the following table of provincial statistics on safety training hours:

What can David conclude from these statistics?

a) The New Brunswick distribution is skewed to the left.

b) The New Brunswick distribution is skewed to the right.

c) The Nova Scotia distribution is skewed to the left.

d) The Nova Scotia distribution is skewed to the right.

e) Both distributions are symmetrical.

Difficulty: Easy

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Application

AACSB: Analytic

85. Manuel Banales, Marketing Director of Plano Power Plants Inc.’s Electrical Division, is leading a study to assess the relative importance of product features. Two items on a survey questionnaire distributed to 100 of Plano’s customers asked them to rate the importance of “ease of maintenance” and “efficiency of operation” on a scale of 1 to 10 (with 1 meaning “not important” and 10 meaning “highly important”). His staff assembled the following statistics on these two items:

What can Manuel conclude from these statistics?

a) The Ease of Maintenance distribution is skewed to the right.

b) The Ease of Maintenance distribution is not skewed.

c) The Efficiency of Operation distribution is skewed to the left.

d) The Efficiency of Operation distribution is positively skewed.

e) Both are symmetrically distributed.

Difficulty: Medium

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Application

AACSB: Analytic

86. 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 20.8 or more

e) 99% of these service stations had sales to inventory ratios of 20.8 or more

Difficulty: Easy

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Application

AACSB: Analytic

87. David Desreumaux, VP of Human Resources of Maritime Boat Manufacturing (MBM), is reviewing the employee training programs of MBM factories. His staff reports several statistics for safety 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 for safety training hours is ___.

a) 6

b) 1

c) 3

d) 4

e) 0

Difficulty: Medium

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Application

AACSB: Analytic

88. David Desreumaux, VP of Human Resources of Maritime Boat Manufacturing (MBM), is reviewing the employee training programs of MBM factories. His staff reports several statistics for safety training hours. The mean is 25 hours, the standard deviation is 7 hours, the median is 40 hours, and mode is 30 hours. Based on this information David can conclude that

a) the distribution is symmetrically distributed

b) the distribution is negatively skewed

c) the distribution is positively skewed

d) the data must have outliers and skewness cannot be determined until more data values are obtained

e) an answer cannot be determined from the information given

Difficulty: Medium

Learning Objective: Describe a data distribution statistically and graphically using skewness, kurtosis, and box-and-whisker plots.

Section Reference: 3.3 Measures of Shape

Blooms: Application

AACSB: Analytic

89. 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.

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.

Blooms: Application

AACSB: Analytic

90. 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

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.

Bloom’s level: Application

AACSB: Analytic

91. 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

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.

Bloom’s level: Knowledge

AACSB: Analytic

92. 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.

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

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.

Blooms: Analysis

AACSB: Analytic

93. 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.

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

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.

Blooms: Analysis

AACSB: Analytic

94. 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.

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

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.

Blooms: Analysis

AACSB: Analytic

95. 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

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.

Blooms: Knowledge

AACSB: Analytic

96. 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

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.

Blooms: Application

AACSB: Analytic

97. 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

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.

Blooms: Application

AACSB: Analytic

98. 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

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.

Blooms: Analysis

AACSB: Analytic

99. 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

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.

Blooms: Analysis

AACSB: Analytic

100. 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

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.

Bloom’s level: Application

AACSB: Analytic

101. 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

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.

Bloom’s level: Analysis

AACSB: Analytic

102. 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%

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.

Bloom’s level: Application

AACSB: Analytic

103. 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%

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.

Bloom’s level: Application

AACSB: Analytic

104. 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

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.

Bloom’s level: Analysis

AACSB: Analytic

105. 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%

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.

Bloom’s level: Application

AACSB: Analytic

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