Deck 3: Numerical Descriptive Measures

Question 1

Mean-variance analysis suggests that investments with lower average returns are also associated with higher risks.

Answer 1

False

Question 2

Outliers are extreme values above or below the mean that require special consideration.

Answer 2

True

Question 3

The empirical rule is only applicable for approximately bell-shaped data.

Answer 3

True

Question 4

The median is not always the 50^th percentile.

Question 5

The geometric mean is a multiplicative average of a data set used to measure values over a period of time.

Question 6

The Sharpe ratio measures the extra reward per unit of risk.

Question 7

The arithmetic mean is the middle value of a data set.

Question 8

Chebyshev's theorem is only applicable for sample data.

Question 9

The formula for a z-score is = .

Question 10

The variance is an average squared deviation from the mean.

Question 11

Mark's grade on the recent business statistics test was an 85 on a scale of 0-100. Based on this information we can conclude that Mark's grade was in the 85^th percentile in his class.

Question 12

The mean absolute deviation (MAD) is a less effective measure of variation when compared with the average deviation from the mean.

Question 13

Z-scores can always be used to detect outliers.

Question 14

In a data set, an outlier is a large or small value regarded as an extreme value in the data set.

Question 15

The coefficient of variation is a unit-free measure of dispersion.

Question 16

The terms central location or central tendency refer to the way quantitative data tend to cluster around some middle or central value.

Question 17

Approximately 60% of the observations in a data set fall below the 60th percentile.

Question 18

The variance and standard deviation are the most widely used measures of central location.

Question 19

The standard deviation is the positive square root of the variance.

Question 20

A box plot is useful when comparing similar information gathered at different places or times.

Question 21

Is it possible for a data set to have no mode?

A) Yes, if two observations occur twice.
B) No, unless there is an odd number of observations.
C) No, if the data set is nonempty, there is always a mode.
D) Yes, if there are no observations that occur more than once.

Question 22

Consider the following data: 1, 2, 4, 5, 10, 12, 18. The 30^th percentile is the closest to ________. (See the Excel Data File.)

A) 2.0
B) 2.4
C) 2.8
D) 5.0

Question 23

How do we find the median if the number of observations in a data set is odd?

A) By averaging the first and the third quartile
B) By taking the middle value in the sorted data set
C) By averaging the minimum and maximum values
D) By taking the middle value in the sorted data set after eliminating outliers

Question 24

The Boom company has recently decided to raise the salaries of all employees by 10%. Which of the following is (are) expected to be affected by this raise?

A) Mean and mode only
B) Mean and median only
C) Mode and median only
D) Mean, median, and mode

Question 25

When working with grouped data, the class median is the value in the middle of the class and can be found by taking the average of the endpoints for each class.

Question 26

Which five values are graphed on a box plot?

A) Min, Quintile 1, Mean, Quintile 3, Max
B) Min, Quartile 1, Mean, Quartile 3, Max
C) Min, Quintile 1, Median, Quintile 3, Max
D) Min, Quartile 1, Median, Quartile 3, Max

Question 27

In what way(s) is(are) the concept of geometric mean useful?

A) In evaluating investment returns
B) In calculating average growth rates
C) In assessing the dispersion of the data
D) Both in evaluating investment returns and in calculating average growth rates

Question 28

In quality control settings, businesses prefer a larger standard deviation, which is an indication of more consistency in the process.

Question 29

The table below gives the deviations of a portfolio's annual total returns from its benchmark's annual returns, for a six-year period ending in Year 6. (See the Excel Data File.) The arithmetic mean return and median return are the closest to ________.

A) mean = -2.00% and median = -4.28%.
B) mean = -2.00% and median = -1.67%.
C) mean = -1.67% and median = -0.56%.
D) mean = -1.67% and median = 0.56%

Question 30

Which of the following statements is most accurate when defining percentiles?

A) The p^th percentile divides a data set into equal parts.
B) Approximately p% of the observations are greater than the p^th percentile.
C) Approximately (100 - p)% of the observations are less than the p^th percentile.
D) Approximately (100 - p)% of the observations are greater than the p^th percentile.

Question 31

The z-score has no units even though the original values will normally be expressed in units such as dollars, years, pounds, or calories.

Question 32

The owner of a company has recently decided to raise the salary of one employee, who was already making the highest salary, by 20%. Which of the following is(are) expected to be affected by this raise?

A) Mean only
B) Median only
C) Mean and median only
D) Mean, median, and mode

Question 33

Geometric mean is greater than the arithmetic mean.

Question 34

As of September 30, the earnings per share (EPS) of five firms in the beverages industry are as follows: (See the Excel Data File.) The 25^th percentile and the 75^th percentile of the EPS are the closest to ________.

A) 0.77 and 1.97
B) 0.91 and 1.77
C) 1.77 and 0.91
D) 1.97 and 0.77

Question 35

The mode is defined as the ________.

A) middle point in a data set.
B) geometric average of a data set.
C) arithmetic average of a data set.
D) most frequent value in a data set.

Question 36

The median is defined as the ________.

A) middle point in a data set.
B) geometric average of a data set.
C) arithmetic average of a data set.
D) most common value of a data set.

Question 37

Calculate the interquartile range from the following data: 1, 2, 4, 5, 10, 12, 18. (See the Excel Data File.)

A) 5
B) 6
C) 10
D) 17

Question 38

Is it possible for a data set to have more than one mode?

A) No, there must always be a single mode, or else there is no mode.
B) Yes, if two or more values in a data set occur the same number of times.
C) Yes, if there are at least two different values in a data set, there is always more than one mode.
D) Yes, if two or more values in a data set occur with the most frequency and the frequency is greater than one.

Question 39

What is the interquartile range?

A) Q3 - Q1
B) Max - Min
C) Mean - Median
D) All values between Q1 and Q3

Question 40

Which of the following is the most influenced by outliers?

A) Mode
B) Median
C) 75th percentile
D) Arithmetic mean

Question 41

What is(are) characteristic(s) of the geometric mean?

A) It is always greater than the arithmetic mean.
B) It is the mathematical equivalent to the median.
C) It is always less than or equal to the arithmetic mean.
D) Both it is the mathematical equivalent to the median and it is always less than or equal to the arithmetic mean.

Question 42

Consider a population with data values of (See the Excel Data File.) The population mean is ________.

A) 12
B) 14
C) 18
D) 22

Question 43

An analyst gathered the following information about the net profit margins of companies in two industries: Compared with the other industry, the relative dispersion of net profit margins is smaller for Industry ________.

A) B, because it has a smaller mean deviation.
B) B, because it has a smaller range of variation.
C) A, because it has a smaller standard deviation.
D) A, because it has a smaller coefficient of variation.

Question 44

What is(are) the most widely used measure(s) of dispersion?

A) Range
B) Interquartile range
C) Variance and standard deviation
D) Covariance and the correlation coefficient

Question 45

Which of the following statements about the mean absolute deviation (MAD) is the most accurate?

A) It is the square root of the standard deviation.
B) It can be a positive number or a negative number.
C) It is measured in the same units as the original data.
D) It is the arithmetic mean of the squared deviations from the mean.

Question 46

A portfolio manager generates a 5% return in Year 1, a 12% return in Year 2, a negative 6% return in Year 3, and a return of 2% in Year 4. The annualized return for the entire period is the closest to ________.

A) 3.05%
B) 3.25%
C) 3.50%
D) 3.77%

Question 47

Which of the following statements about variance is the most accurate?

A) Variance is the square root of the standard deviation.
B) Variance can be both, positive or negative.
C) Variance is denominated in the same units as the original data.
D) Variance is the average of the squared deviations from the mean.

Question 48

Consider a population with data values of (See the Excel Data File.) The population variance is the closest to ________.

A) 8.00
B) 8.64
C) 64.00
D) 74.67

Question 49

Consider a population with data values of (See the Excel Data File.) The median is ________.

A) 12
B) 14
C) 18
D) 22

Question 50

The sample data below shows the number of hours spent by five students over the weekend to prepare for Monday's Business Statistics exam. (See the Excel Data File.) The sample standard deviation of the number of hours spent by the five students is the closest to ________.

A) 3.6 hours
B) 4.1 hours
C) 13.2 hours
D) 16.5 hours

Question 51

Consider a population with data values of (See the Excel Data File.) The mode is ________.

A) 12
B) 14
C) 18
D) 22

Question 52

The following data represent monthly returns (in percent): (See the Excel Data File.) The geometric mean return is the closest to ________.

A) -0.43%
B) 0.78%
C) 0.94%
D) 4.79%

Question 53

The range is defined as ________.

A) Q3 - Q1
B) Max - Q1
C) Max - Min
D) Max - Median

Question 54

What is the relationship between the variance and the standard deviation?

A) The standard deviation is the absolute value of the variance.
B) The variance is the absolute value of the standard deviation.
C) The variance is the positive square root of the standard deviation.
D) The standard deviation is the positive square root of the variance.

Question 55

The sample data below shows the number of hours spent by five students over the weekend to prepare for Monday's Business Statistics exam. (See the Excel Data File.) The 75^th percentile of the data is the closest to ________.

A) 3 hours
B) 4.5 hours
C) 8.5 hours
D) 10 hours

Question 56

Sales for Adidas grew at a rate of 0.5196 in Year 1, 0.0213 in Year 2, 0.0485 in Year 3, and -0.0387 in Year 4. The average growth rate for Adidas during these four years is the closest to ________.

A) 3.49%
B) 11.83%
C) 13.77%
D) 14.02%

Question 57

The sample data below shows the number of hours spent by five students over the weekend to prepare for Monday's Business Statistics exam. (See the Excel Data File.) The interquartile range of the data is the closest to ________.

A) 4 hours
B) 6 hours
C) 10 hours
D) 12 hours

Question 58

Total revenue for Apple Computers (in millions) was $42,905 in Year 1, $65,225 in Year 2, and $108,249 in Year 3. The average growth rate of revenue during these three years is the closest to ________.

A) 36.13%
B) 39.33%
C) 58.84%
D) 58.99%

Question 59

Consider a population with data values of (See the Excel Data File.) The population standard deviation is the closest to ________.

A) 8.00
B) 8.64
C) 64.00
D) 74.67

Question 60

The sample data below shows the number of hours spent by five students over the weekend to prepare for Monday's Business Statistics exam. (See the Excel Data File.) The mean and the median of the numbers of hours spent by the five students are ________.

A) 2 hours and 3 hours, respectively
B) 3 hours and 5 hours, respectively
C) 5 hours and 2 hours, respectively
D) 5 hours and 3 hours, respectively

Question 61

A college professor collected data on the number of hours spent by his 100 students over the weekend to prepare for Monday's Business Statistics exam. He processed the data by Excel and the following incomplete output is available. The median is most likely to be ________.

A) about 7 hours
B) less than 7 hours
C) greater than 7 hours
D) Cannot tell from the information provided

Question 62

The advantage of using mean absolute deviation rather than variance as a measure of dispersion is that mean absolute deviation ________.

A) is less sensitive to extreme deviations
B) requires fewer observations to be a valid measure
C) is a relative measure rather than an absolute measure of risk
D) considers only unfavorable (negative) deviations from the mean

Question 63

The annual returns (in percent) for a sample of stocks in the technology industry over the past year are as follows: (See the Excel Data File.) The average return is the closest to ________.

A) -6.6
B) -5
C) 0
D) 2.8

Question 64

A college professor collected data on the number of hours spent by his 100 students over the weekend to prepare for Monday's Business Statistics exam. He processed the data by Excel and the following incomplete output is available. The coefficient of variation in the data is ________.

A) 40%
B) 90%
C) 111%
D) 243%

Question 65

The price to earnings ratio, also called the P/E ratio of a stock, is a measure of the price of a share relative to the annual net income per share earned by the firm. Suppose the P/Es for a firm's common stock during the past four quarters are 10, 12, 15, and 11, respectively. The standard deviation of the P/E ratio over the four quarters is ________.

A) 1.87
B) 2.16
C) 3.50
D) 4.67

Question 66

The coefficient of variation is best described as ________.

A) a relative measure of dispersion
B) an absolute measure of dispersion
C) a relative measure of central location
D) an absolute measure of central location

Question 67

A bowler's scores for a sample of six games were (See the Excel Data File.) The bowler's average score is ________.

A) 172
B) 174
C) 178
D) 190

Question 68

A bowler's scores for a sample of six games were The bowler's modal score is ________.

A) 172
B) 174
C) 178
D) 190

Question 69

For k > 1, Chebyshev's theorem is useful in estimating the proportion of observations that fall within ________.

A) k standard deviations from the mean
B) k² standard deviations from the mean
C) (1 - 1/k) standard deviations from the mean
D) (1 - 1/k²) standard deviations from the mean

Question 70

A portfolio's annual total returns (in percent) for a five-year period are: (See the Excel Data File.) The median and the standard deviation for this sample are the closest to ________.

A) 0.75 and 5.46
B) 1.62 and 5.46
C) 1.62 and 6.11
D) 2.50 and 6.11

Question 71

The annual returns (in percent) for a sample of stocks in the technology industry over the past year are as follows: (See the Excel Data File.) The median return is the closest to ________.

A) -6.6
B) -5
C) 0
D) 2.8

Question 72

A bowler's scores for a sample of six games were (See the Excel Data File.) The bowler's median score is ________.

A) 172
B) 174
C) 178
D) 190

Question 73

The annual returns (in percent) for a sample of stocks in the technology industry over the past year are as follows: (See the Excel Data File.) The sample standard deviation is the closest to ________.

A) 7.59
B) 8.49
C) 57.61
D) 72.01

Question 74

The following table summarizes selected statistics for two portfolios for a 10-year period. Assume that the risk-free rate is 4% over this period. As measured by the Sharpe ratio, the fund with the superior risk-adjusted performance during this period is ________.

A) Fund A because it has a lower positive Sharpe ratio than Fund B
B) Fund B because it has a lower positive Sharpe ratio than Fund A
C) Fund A because it has a higher positive Sharpe ratio than Fund B
D) Fund B because it has a higher positive Sharpe ratio than Fund A

Question 75

As of September 30, the earnings per share (EPS) of five firms in the biotechnology industry are (See the Excel Data File.) The sample mean and the sample standard deviation are the closest to ________.

A) 1.53 and 0.76
B) 1.53 and 0.87
C) 1.69 and 0.76
D) 1.69 and 0.87

Question 76

The mean return on equity (ROE) for a group of firms in an industry is 15% with a variance of 9%. The coefficient of variation of the industry's ROE is ________.

A) 0.2
B) 0.6
C) 1.7
D) 5.0

Question 77

Which are characteristic(s) of the coefficient of variation?

A) It adjusts for differences in the magnitude of means.
B) It has the same units of measurement as the observations.
C) It allows for direct comparisons across different data sets.
D) Both it adjusts for differences in the magnitude of means and it allows for direct comparisons across different data sets.

Question 78

The Sharpe ratio measures ________.

A) the extra reward per unit of risk
B) the extra risk per unit of reward
C) the increase in mean per unit of risk
D) the extra variance per unit of reward

Question 79

Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. With the beginning of the next academic year, all professors will get a 2% raise. What will be the average and the standard deviation of their new salaries?

A) $80,000 and $6,120.
B) $81,600 and $6,000.
C) $81,600 and $6,120.
D) $82,000 and $6,200.

Question 80

The table below gives statistics relating to a hypothetical 10-year record of two portfolios. Assume other statistics relating to these portfolios are the same and the risk-free rate is 3.5%. Using the coefficient of variation and the Sharpe ratio, the fund that is preferred in terms of relative risk and return per unit of risk is ________.

A) Portfolio A because it has a higher coefficient of variation and a lower Sharpe ratio
B) Portfolio A because it has a lower coefficient of variation and a higher Sharpe ratio
C) Portfolio B because it has a higher coefficient of variation and a lower Sharpe ratio
D) Portfolio B because it has a lower coefficient of variation and a higher Sharper ratio