Deck 3: Descriptive Statistics

Question 1

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

Answer 1

False

Question 2

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

Answer 2

False

Question 3

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

Answer 3

False

Question 4

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.

Question 5

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

Question 6

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

Question 7

Measures of variability include percentiles and quartiles.

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

The coefficient of variation is unitless.

Question 14

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

Question 15

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.

Question 16

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

Question 17

Percentiles divide a group of data into 99 parts

Question 18

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

Question 19

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

Question 20

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.

Question 21

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

Question 22

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

Question 23

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.

Question 24

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

Question 25

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

Question 26

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

Question 27

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.

Question 28

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

Question 29

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

Question 30

An outlier of a data set is determined from the lower and upper quartile

Question 31

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

Question 32

If the mean, median, and mode are equal, then the distribution is positively skewed.

Question 33

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.

Question 34

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

Question 35

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

Question 36

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

Question 37

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.

Question 38

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

Question 39

Skewness indicates that a data distribution is symmetrical or asymmetrical.

Question 40

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

Question 41

The following twelve data values are provided: The value of Q₁ is _____

A)184.5
B)187
C)215.5
D)440
E)578

Question 42

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

Question 43

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

Question 44

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

Question 45

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

Question 46

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%

Question 47

The following twelve data values are provided: The 80^th percentile is _____

A)187
B)244
C)302
D)440
E)578

Question 48

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

Question 49

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

Question 50

The following ten data values are provided: The 80^th percentile is _____

A)984
B)995
C)1609
D)2346
E)3083

Question 51

The following twelve data values are provided: The value of Q₃ is _____

A)7739
B)7596
C)6188
D)6032
E)5352

Question 52

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

Question 53

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

Question 54

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%

Question 55

The following ten data values are provided: The value of Q₁ is _____

A)973
B)984
C)995
D)1609
E)3083

Question 56

The following twelve data values are provided: The 30^th percentile is _____

A)187
B)244
C)250
D)302
E)578

Question 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

Question 58

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%

Question 59

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

Question 60

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

Question 61

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

Question 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 standard deviation for this sample data?

A)3.32
B)2.97
C)1.73
D)11
E)-1.4

Question 63

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

Question 64

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

Question 65

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

Question 66

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

Question 67

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

Question 68

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

Question 69

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

Question 70

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

Question 71

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

Question 72

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%

Question 73

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

Question 74

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%

Question 75

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%

Question 76

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

Question 77

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

Question 78

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

Question 79

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%

Question 80

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