Deck 3: Descriptive Statistics II: Additional Descriptive Measures and Data Displays

Question 1

The correlation coefficient cannot be greater than 1.0.

Answer 1

True

Question 2

The interquartile range is used as a measure of variability to overcome what difficulty of the range?

A)the sum of the range variances is zero
B)the range is difficult to compute
C)the range is influenced too much by extreme values
D)the range is negative
E)none of the above

Answer 2

the range is influenced too much by extreme values

Question 3

The coefficient of variation is the preferred measure of dispersion when comparing the dispersion in data sets that have different means.

Answer 3

True

Question 4

If a data value has a z-score of -2.75 then it is considered an outlier.

Question 5

The interquartile range is the difference between the 75 percentile and the 25 percentile values in a data set.

Question 6

The correlation coefficient cannot be negative.

Question 7

The geometric mean is appropriate any time the values being averaged are of unequal importance.

Question 8

Halston Communications (HC) hired 120 new workers last year.This put the company at the first quartile value among all firms in the greater Houston area.Explain what this means.

A)At least 25% of Houston companies hired 120 or more new workers.
B)At least 75% of Houston companies hired 120 or more new workers.
C)At least 75% of Houston companies hired 120 or fewer new workers.
D)At least 25% of the new hires in the greater Houston area were by HC.
E)At least 50% of Houston companies hired 75% new workers.

Question 9

When calculating the p^th percentile, if the index i is NOT an integer then take the average of the data values in the i - 1 and i + 1 positions.

Question 10

Positive values of the covariance indicate a positive relation between the x and the y variables.

Question 11

In computing the p^th percentile, if the index i is NOT an integer the p^th percentile is the:

A)average of data values in position i and i+1.
B)data value in the position denoted by the next integer greater than i.
C)data value in position i.
D)data value in position i+1.
E)none of the above.

Question 12

The empirical rule states that approximately 95.9% of values in a data set will be within two standard deviations of the mean if the data follows a bell-shaped curve.

Question 13

The correlation coefficient is a standardized value that ranges between -1 and +1.

Question 14

The width of the box in a box-and-whisker plot is the interquartile range (IQR).

Question 15

In computing the pth percentile, if the index i is NOT an integer, then round up to the next highest integer to get the pth percentile.

Question 16

A stem-and-leaf display is a graph of a cumulative distribution.

Question 17

An outlier is a data value that has a z-score less than -1.5 or is greater than Q3-1.5*IQR.

Question 18

The 50^th percentile of a data set:

A)cannot be larger than the mean of the data set.
B)will tend to be larger than the mean of the data set if the distribution is negatively skewed.
C)will tend to be larger than the mean of the data set if the distribution is positively skewed.
D)will always be less than or equal to Q1.
E)none of the above.

Question 19

The interquartile range measures the middle 65% of the values in the data set.

Question 20

The interquartile range is the difference between the third quartile and the first quartile values in the data set.

Question 21

In July 2013, the unemployment rate in California was 8.5%, that of Oregon was 7.9%, and that of Washington State was 6.8%.(Keep in mind that California is by far the most populous of the three states).If a simple, rather than weighted, average were used to estimate the overall unemployment rate across the three West coast states, the resulting value would be:

A)an underestimate of the true unemployment rate across the three states.
B)an accurately estimate of the true unemployment rate across the three states.
C)an overestimate of the true unemployment rate across the three states.
D)the direction of the bias of the estimate cannot be determined.
E)none of the above

Question 22

Which of the following denotes the number of standard deviations a data value is from the mean?

A)range
B)median
C)z-score
D)third quartile
E)variance

Question 23

Which of the following best describes the correlation coefficient?

A)it is a standardized measure and can take on values from -1 to +1
B)it is the covariance of two variables divided by the product of the individual standard deviations
C)values near -1 represent a strong negative linear relationship
D)for samples it is denoted by r_xy
E)all of the above

Question 24

If the interquartile range of a data set is zero,

A)the middle 50% of the values in the data set are zero.
B)the middle 50% of the values in the data set are the same.
C)the range of the data set must also be zero.
D)the median of the data set must also be zero.
E)the mean of the data set must also be zero.

Question 25

Which of the following approaches can be used to identify outliers?

A)1.5*IQR (interquartile range)
B)empirical rule
C)z-score
D)all of the above
E)none of the above

Question 26

Which of the following statements is NOT true regarding the z-score?

A)it can be calculated as the data value minus the mean divided by the variance
B)it is a standardized value (has no units)
C)it denotes the number of standard deviations a data value is from the mean
D)a data value less than the mean will have a z-score less than zero
E)a data value with a z-score less than -3 or greater than +3 might be considered an outlier

Question 27

A graphical device for depicting the relationship between two quantitative variables is a(n):

A)histogram
B)stem-and-leaf diagram
C)scatter diagram
D)bar graph
E)box plot

Question 28

The interquartile range for a set of data can be described as the range of the middle ___ % of the values in the data set.

A)75
B)50
C)25
D)90
E)60

Question 29

Which of the following statements is TRUE concerning the correlation coefficient?

A)it can take on values between -1 and +1.
B)it is a standardized value (has no units).
C)values near -1 indicate a strong negative linear relationship.
D)values near 0 indicate little or no relationship.
E)all of the above

Question 30

A coffee shop finds that the correlation between daily high temperature and daily sales is -0.74.The interpretation of this value is as follows:

A)The value of sales falls approximately $0.74 for each degree that the temperature increases.
B)The slope of the linear relationship between temperature and sales is -0.74; there is a negative relation between the two.
C)There is a negative association between temperature and sales: as the temperature falls, sales tend to decrease.
D)There is a negative association between temperature and sales: as the temperature falls, sales tend to increase.
E)There is a negative association between temperature and sales: as the temperature falls, sales tend to decrease by $0.74.

Question 31

Which of the following best describes the coefficient of variation?

A)it measures variation as a percentage of the mean.
B)it calculated as the mean divided by the standard deviation.
C)it is not helpful when comparing the dispersion in data sets that have different means
D)it can only be calculate using population parameters, not sample statistics
E)all of the above

Question 32

In a box plot, the median of the observations:

A)lies exactly in the center of the box.
B)is where the line is drawn inside the box.
C)is sometimes contained within the box.
D)may fall inside or outside of the box.
E)none of the above

Question 33

A graphical device for depicting qualitative data that have been summarized in a frequency distribution or a relative frequency distribution is a(n):

A)histogram
B)stem-and-leaf diagram
C)ogive
D)bar graph
E)box plot

Question 34

Which of the following best describes a stem-and-leaf diagram?

A)it is a kind of sideways histogram.
B)it gives a visual sense of the shape, center, and dispersion of the data.
C)it can identify significant clusters of values.
D)it can help to identify outliers.
E)all of the above

Question 35

The five number summary is used to produce which of the following graphical charts, diagrams, or plots:

A)a pie chart
B)a histogram
C)a stem-and-leaf diagram
D)a box plot
E)a scatter diagram

Question 36

Compared to the range, the interquartile range:

A)is less affected by extreme values.
B)is more affected by extreme values.
C)is likely to be closer to the value of the mean.
D)is likely to be closer to the value of the median.
E)is likely to be closer to the value of the mode.

Question 37

Which of the following is TRUE regarding the covariance?

A)a positive covariance means that the two variables move in the same direction.
B)a negative covariance means that the two variables move in opposite directions.
C)a covariance of zero indicates no linear association at all.
D)it is denoted by $\sigma$ _xy
E)all of the above

Question 38

Studies have shown that the number of fire engines at a fire and the amount of damage done by the fire are highly and positively correlated.Which of the following conclusions seems most appropriate?

A)send as few fire engines to a fire as possible.
B)the presence of more fire engines tends to cause more confusion, leading to greater fire damage.
C)the number of fire engines and the amount of fire damage are both related to a third factor-the size of the fire-and so are correlated to one another.
D)fires and fire engines have something in common - they are both red.
E)none of the above

Question 39

Which of the following can be used to determine the percentage of data values that must be within one, two, and three standard deviations of the mean for data having a bell-shaped distribution?

A)Chebyshev's theorem
B)the empirical rule
C)the five-number summary
D)a box plot
E)the interquartile range

Question 40

The correlation of two variables, x and y, is -0.95.This means that:

A)as x increases, y tends to increase, and the relationship between the two is nearly linear.
B)as x decreases, y tends to increase, and the relationship between the two variables is nearly linear.
C)as x increases, y tends to decrease, and the slope of the relationship between x and y is approximately -0.05.
D)an increase in x causes a fall in y.
E)none of the above

Question 41

Below is a list of the total attendance at the Portland Oaks 25 home basketball games this season.Determine the 35th percentile value. 194, 198, 223, 211, 230, 221, 190, 185, 234, 210, 189, 193, 198,
178, 209, 231, 186, 203, 182, 193, 201, 242, 216, 177, 204

A)195.5
B)196
C)193
D)201
E)191

Question 42

Below is a list of the total attendance at the Portland Oaks 25 home basketball games this season.Determine the 60th percentile value. 194, 198, 223, 211, 230, 221, 190, 185, 234, 210,189, 193, 198,
178, 209, 231, 186, 203, 182, 193, 201, 242, 216, 177, 204

A)206.5
B)201.5
C)210.5
D)205
E)198.5

Question 43

The data below indicate the number of "green" homes built in 10 selected metropolitan areas during the past year.Determine the 20^th percentile value for the data.

A)1122.5
B)1058.5
C)1158.0
D)1097.5
E)1134.0

Question 44

A __________ visually shows the relationship between two quantitative variables.

A)box plot
B)stem-and-leaf diagram
C)a scatter diagram
D)a bar chart
E)a histogram

Question 45

The ____________ measures variation as a percentage of the mean.

A)weighted average
B)coefficient of variation
C)standard deviation
D)covariance
E)correlation coefficient

Question 46

The data below indicate the number of "green" homes built in 10 selected metropolitan areas during the past year.Determine the median number of green homes built in the sampled areas.

A)2150
B)1860
C)1755
D)1650
E)1970

Question 47

The table below shows the advertising expenditures in $millions for the nine largest tech companies during the past year.Determine the median advertising expenditure.

A)175.8
B)181.2
C)156.4
D)169.6
E)190.5

Question 48

Below is a list of the total attendance at the Portland Oaks 25 home basketball games this season.Determine the median value. 194, 198, 223, 211, 230, 221, 190, 185, 234, 210, 189, 193, 198,
178, 209, 231, 186, 203, 182, 193, 201, 242, 216, 177, 204

A)203
B)201
C)204.5
D)198
E)196.5

Question 49

The data below indicate the number of "green" homes built in 10 selected metropolitan areas during the past year.Determine the 75^th percentile value for the data.

A)2600
B)2750
C)2855
D)2800
E)2875

Question 50

The table below shows the advertising expenditures in $millions for the nine largest tech companies during the past year.Determine the 25^th percentile or first quartile value here.

A)138.6
B)146.5
C)122.5
D)119.0
E)133.8

Question 51

The table below shows the advertising expenditures in $millions for the nine largest tech companies during the past year.Determine the 75^th percentile or third quartile value here.

A)183.4
B)196.1
C)165.9
D)187.3
E)179.6

Question 52

The __________ is a standardized measure and can take on values from -1 to +1.

A)correlation coefficient
B)covariance
C)z-score
D)standard deviation
E)coefficient of variation

Question 53

The list below shows the number of orders processed by Grant and Traynor over the past 16 weeks. Use the method described in the chapter to identify the value of the 65th percentile, then compare the % of the values in the data set that are ACTUALLY at or below the 65th percentile value you had determined.

A)The 65th percentile value is 472; the actual percent of the values at or below 472 is 75.00%.
B)The 65th percentile value is 660; the actual percent of the values at or below 660 is 68.75%.
C)The 65th percentile value is 660; the actual percent of the values at or below 660 is 37.5%.
D)The 65th percentile value is 472; the actual percent of the values at or below 472 is 31.25%.
E)The 65th percentile value is 531; the actual percent of the values at or below 472 is 65.00%.

Question 54

The table below shows the number of customer complaints received by the customer service hotline at Kendall Products during the past 6 days. _____% of the values in this data set actually fall within plus or minus two standard deviations of the mean.

A)83.3
B)50.0
C)99.7
D)68.3
E)33.3

Question 55

In a recent survey, 18 college freshmen were asked how many text messages they had send or received on the day of the survey.Results are shown below.Determine the median value. 45, 256, 23, 110, 168, 122, 135, 56, 18, 0, 44, 68, 120, 115, 456, 256, 174, 88

A)110
B)106.5
C)120
D)115.5
E)112.5

Question 56

In a recent survey, 18 college freshmen were asked how many text messages they had send or received on the day of the survey.Results are shown below.Determine the 40th percentile value. 45, 256, 23, 110, 168, 122, 135, 56, 18, 0, 44, 68, 120, 115, 456, 256, 174, 88

A)45
B)110
C)88
D)100
E)80.5

Question 57

The table below shows the number of customer complaints received by the customer service hotline at Kendall Products during the past 6 days. _____% of the values in this data set actually fall within plus or minus four standard deviations of the mean.

A)50
B)66
C)95
D)100
E)25

Question 58

The list below shows the number of orders processed by Grant and Traynor over the past 16 weeks. Use the method described in the chapter to identify the value of the 30th percentile, then compare the % of the values in the data set that are ACTUALLY at or below the 30th percentile value you had determined.

A)The 30th percentile value is 660; the actual percent of the values at or below 660 is 37.5%.
B)The 30th percentile value is 660; the actual percent of the values at or below 660 is 68.75%.
C)The 30th percentile value is 472; the actual percent of the values at or below 472 is 31.25%.
D)The 30th percentile value is 472; the actual percent of the values at or below 472 is 75.00%.
E)The 30th percentile value is 531; the actual percent of the values at or below 472 is 30.00%.

Question 59

In a recent survey, 18 college freshmen were asked how many text messages they had send or received on the day of the survey.Results are shown below.Determine the 85th percentile value. 45, 256, 23, 110, 168, 122, 135, 56, 18, 0, 44, 68, 120, 115, 456, 256, 174, 88

A)250
B)270.5
C)174
D)256
E)210.5

Question 60

A __________ makes use of the five number summary.

A)box plot
B)stem-and-leaf diagram
C)a scatter diagram
D)a bar chart
E)a histogram

Question 61

The heights in inches of the 14 players listed on the Chicago Bulls roster for the 2013-14 season are shown below (NBA.com).Find the interquartile range. 81, 79, 77, 81, 81, 81, 76, 82, 82, 82, 83, 75, 79, 74.

A)1
B)5
C)7.5
D)9
E)11.4

Question 62

Player payrolls for the top 20 teams in professional baseball are shown in the table below.Identify the 1st quartile value.

A)86.05
B)77.25
C)92.81
D)97.08
E)89.50

Question 63

In a test of RiteAid.com's new website, search times for 20 trial orders were recorded, in minutes.Results are reported in the table: Construct an ORDERED stem-and-leaf diagram for the data.One of the rows in the table would look like:

A)1 l 2 4 4 5 6 9
B)3 l 2 5 6 8
C)1 l 2 3 4 4 8 9
D)2 l 2 3 4 4 5 6
E)2 l 2 3 4 4 5 7

Question 64

The table below shows test scores for 11 students in Accounting 512.Identify the interquartile range (IR).

A)15
B)17
C)13.5
D)22.5
E)13

Question 65

The table below shows test scores for 11 students in Accounting 512.Identify the 3rd quartile value.

A)76.5
B)68
C)79
D)76
E)73

Question 66

The number of base hits for the top 26 rookies in the American League last season are given below.Determine the interquartile range for the data. 124, 141, 132, 111, 115, 135, 152, 121, 132, 125, 119, 123, 98,
140, 127, 132, 108, 122, 135, 141, 120, 118, 163, 121,138, 122

A)15
B)16.7
C)14.4
D)17
E)14

Question 67

The data below show the number of new jobs created in Georgia's 20 most populous counties during the past month. Create a stem-and-leaf diagram to display the data using two leading digits to form the stem.Use a "leaf unit" of 10 so that you can construct the diagram using only one-digit leaves.Make your diagram an "ordered" stem-and-leaf diagram by putting the leaf values in ascending order.In your diagram, the row in which "1" and "8" are the 2 leading digits should look like:

A)18 l 1 1 8 9 9
B)18 l 1 1 8 8 9
C)18 l 1 8 8 8 9
D)18 l 1 8 8 9 9
E)18 l 1 7 8 9 9

Question 68

The heights in inches of the 14 players listed on the Chicago Bulls roster for the 2013-14 season are shown below (NBA.com).Determine the 25^th percentile value. 81, 79, 77, 81, 81, 81, 76, 82, 82, 83, 82, 75, 79, 74.

A)3.5
B)20.75
C)77
D)81
E)85.5

Question 69

The table below shows test scores for 11 students in Accounting 512.Identify the 1st quartile value.

A)56
B)40
C)47
D)53
E)68

Question 70

The data below show the number of new jobs created in Georgia's 20 most populous counties during the past month. Create a stem-and-leaf diagram to display the data using two leading digits to form the stem.Use a "leaf unit" of 10 so that you can construct the diagram using only one-digit leaves.Retain the original order when entering the leaf values.In your diagram, the row in which "1" and "7" are the 2 leading digits should look like:

A)17 l 5 1 1 0 1 1 0
B)17 l 0 0 0 1 5 1 0
C)17 l 5 0 0 1 1 1 0
D)17 l 1 0 0 5 1 1 0
E)17 l 1 0 2 5 1 1 3

Question 71

The data below shows closing share prices for today's most actively traded stocks on the NYSE.Determine the interquartile range for the data. 22.1, 23.5, 26.8, 15.5, 13.6, 28.9, 14.5, 36.0, 27.8,
25)2, 35.7, 62.5, 16.2, 35.5, 28.2, 15.6, 32.7, 12.7

A)15.5
B)16.4
C)17.1
D)18.3
E)19.5

Question 72

Player payrolls for the top 20 teams in professional baseball are shown in the table below.Identify the 2nd quartile value.

A)175.4
B)161.8
C)156.2
D)169.7
E)179.4

Question 73

The table below shows test scores for 11 students in Accounting 512.Identify the 2nd quartile value.

A)73
B)57
C)72
D)70
E)68

Question 74

Below is a list of file sizes (in gigabytes) for 15 data files that Ron DiGregorio created for his updated customer records.Determine the value of Q2.

A)3.2
B)3.6
C)6.0
D)5.5
E)5.2

Question 75

The heights in inches of the 14 players listed on the Chicago Bulls roster for the 2013-14 season are shown below (NBA.com).Find the value of Q3. 81, 79, 77, 81, 81, 81, 76, 82, 82, 82, 83, 75, 79, 74.

A)10.5
B)77
C)82
D)83
E)85.5

Question 76

In a test of RiteAid.com's new website, search times for 20 trial orders were recorded, in minutes.Results are reported in the table: Construct a proper stem-and-leaf diagram for the data.One of the rows in the table would look like:

A)1 l 2 6 4 4 9 3
B)2 l 2 4 5 4 2 4 6
C)3 l 5 6 2 7
D)2 l 2 4 6 4 3 5 6
E)2 l 2 4 5 6 3 5 6

Question 77

Below is a list of file sizes (in gigabytes) for 15 data files that Ron DiGregorio created for his updated customer records.Determine Q3.

A)7.8
B)6.0
C)6.2
D)6.5
E)8.9

Question 78

Below is a list of file sizes (in gigabytes) for 15 data files that Ron DiGregorio created for his updated customer records.Determine the value of Q1.

A)3.6
B)3.2
C)4.5
D)5.5
E)4.25

Question 79

Player payrolls for the top 20 teams in professional baseball are shown in the table below.Identify the 3rd quartile value.

A)366.81
B)354.22
C)359.68
D)377.36
E)382.55

Question 80

The heights in inches of the 14 players listed on the Chicago Bulls roster for the 2013-14 season are shown below (NBA.com).Determine the median value. 81, 79, 77, 81, 81, 81, 76, 82, 82, 83, 82, 75, 79, 74.

A)7
B)79
C)79.5
D)81
E)85.5