Deck 3: Numerical Descriptive Measures

Question 1

The geometric mean is a multiplicative average of a data set.

Answer 1

True

Question 2

Chebyshev's theorem is only applicable for sample data.

Answer 2

False

Question 3

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

Answer 3

False

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

The variance is an average squared deviation from the mean.

Question 13

The median is defined as…

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

Question 14

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

Question 15

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 16

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

Question 17

The median is not always the 50^th percentile.

Question 18

Which of the following is most influenced by outliers?

A)Mode
B)Median
C)75^th Percentile
D)Arithmetic mean

Question 19

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

Question 20

The mode is defined as…

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

Question 21

Total Revenue,in $millions,for Apple Computers was 42,905 in 2009,65,225 in 2010,and 108,249 in 2011.The average growth rate of revenue during these three years is closest to:

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

Question 22

How do you define the range?

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

Question 23

Consider the following data: 1,2,4,5,10,12,18.The 30^th percentile is closest to:

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

Question 24

As of September 30,2011,the earnings per share,EPS,of five firms in the beverages industry are as follows: The 25^th percentile and the 75^th percentile of the EPS are closest to:

A)Option A
B)Option B
C)Option C
D)Option D

Question 25

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 26

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

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

Question 27

Calculate the interquartile range from the following data: 1,2,4,5,10,12,18.

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

Question 28

The table below gives the deviations of a portfolio's annual total returns from its benchmark's annual returns,for a 6-year period ending in 2011. The arithmetic mean return and median return are closest to:

A)Option A
B)Option B
C)Option C
D)Option D

Question 29

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 30

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 31

In what way(s)is 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 A and B

Question 32

The following data represent monthly returns (in percent): The geometric mean return is closest to:

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

Question 33

Sales for Adidas grew at a rate of 0.5196 in 2006,0.0213 in 2007,0.0485 in 2008,and -0.0387 in 2009.The average growth rate for Adidas during these four years is closest to:

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

Question 34

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 35

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 36

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

A)The pth 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 37

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 38

What is the interquartile range?

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

Question 39

The Boom company has recently decided to raise the salaries of all employees by 10 percent.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 40

A portfolio manager generates a 5% return in 2008,a 12% return in 2009,a negative 6% return in 2010,and a return of 2% (non-annualized)in the first quarter of 2011.The annualized return for the entire period is closest to:

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

Question 41

The sample data below shows the number of hours spent by 5 students over the weekend to prepare for Monday's Business Statistics exam. The sample standard deviation of the number of hours spent by the 5 students is closest to:

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

Question 42

Consider a population with data values of . The population variance is closest to:

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

Question 43

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 44

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

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

Question 45

A bowler's scores for a sample of six games were The bowler's average score is:

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

Question 46

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 47

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 48

The sample data below shows the number of hours spent by 5 students over the weekend to prepare for Monday's Business Statistics exam. The mean and the median of the numbers of hours spent by the 5 students are

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

Question 49

Consider a population with data values of . The median is:

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

Question 50

The sample data below shows the number of hours spent by 5 students over the weekend to prepare for Monday's Business Statistics exam. The 75^th percentile of the data is closest to:

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

Question 51

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

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

Question 52

Consider a population with data values of . The mode is:

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

Question 53

The sample data below shows the number of hours spent by 5 students over the weekend to prepare for Monday's Business Statistics exam. The interquartile range of the data is closest to:

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

Question 54

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

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

Question 55

A bowler's scores for a sample of six games were The bowler's median score is:

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

Question 56

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

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

Question 57

Consider a population with data values of . The population standard deviation is closest to:

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

Question 58

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 59

Consider a population with data values of . The population mean is:

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

Question 60

A bowler's scores for a sample of six games were The sample standard deviation is closest to:

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

Question 61

A portfolio's annual total returns (in percent)for a 5-year period are: The median and the standard deviation for this sample are closest to:

A)Option A
B)Option B
C)Option C
D)Option D

Question 62

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

Question 63

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 be 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 64

In its standard form,Chebyshev's theorem provides a lower bound on:

A)The number of observations lying within a certain interval.
B)The number of observations lying outside a certain interval.
C)The proportion (or percentage)of observations lying within a certain interval.
D)The proportion (or percentage)of observations lying outside a certain interval.

Question 65

When applicable,the empirical rule provides the approximate percentage of observations that fall within how many standard deviations from the mean?

A)1,2,or 3 standard deviations
B)2,3,or 4 standard deviations
C)k standard deviations for every k > 1
D)1 - 1/k² standard deviations for every k > 1

Question 66

The empirical rule can be used to estimate some proportions when data has what shape?

A)Any shape
B)When it is skewed to the left
C)When it is skewed to the right
D)When it is approximately symmetric and bell-shaped

Question 67

Chebyshev's theorem is applicable when the data are

A)Any shape
B)Skewed to the left
C)Skewed to the right
D)Approximately symmetric and bell-shaped

Question 68

What capabilities do Chebyshev's theorem and the empirical rule provide?

A)They make statements regarding the shape of the data.
B)They make statements regarding the central location of the data.
C)They make statements regarding the dispersion of the data around the median.
D)They make statements regarding the percentage of data values that fall within some number of standard deviations from the mean.

Question 69

What is the difference between Chebyshev's theorem and the empirical rule?

A)The empirical rule applies to all data sets,whether their distributions are symmetric and bell-shaped or not.
B)Chebyshev's theorem applies to all data sets except those that have approximately a symmetric and bell-shaped distribution.
C)The empirical rule applies to all data sets,whereas Chebyshev's theorem is appropriate when the data have approximately a symmetric and bell-shaped distribution.
D)Chebyshev's theorem applies to all data sets,whereas the empirical rule is only appropriate when the data have approximately a symmetric and bell-shaped distribution.

Question 70

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 71

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 72

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 73

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

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

Question 74

When using the empirical rule,which assumption is made?

A)The data only comes from a sample.
B)The data only comes from a population.
C)The data is exactly symmetric and bell-shaped.
D)The data is approximately symmetric and bell-shaped.

Question 75

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 76

In an accounting class of 200 students,the mean and standard deviation of scores was 70 and 5,respectively.Use the empirical rule to determine the number of students who scored less than 65 or more than 75.

A)about 32
B)about 64
C)about 68
D)about 136

Question 77

In a marketing class of 60 students,the mean and the standard deviation of scores was 70 and 5,respectively.Use Chebyshev's Theorem to determine the number of students who scored less than 60 or more than 80:

A)At least 45
B)At most 15
C)At most 45
D)At least 15

Question 78

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 79

Which of the following is true when using the empirical rule for a set of sample data?

A)Almost all observations are in the interval .
B)Approximately 68% of all observations are in the interval .
C)Approximately 95% of all observations are in the interval .
D)Approximately 68% of all observations are in the interval

Question 80

As of September 30,2011,the earnings per share,EPS,of five firms in the biotechnology industry are as follows: The sample mean and the sample standard deviation are closest to:

A)Option A
B)Option B
C)Option C
D)Option D