# Quiz 4: Numerical Descriptive Techniques

Statistics

Q 1Q 1

Statisticians typically apply graphical techniques as a first step in a data analysis because we first need to know the shape of the distribution.

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True False

True

Q 2Q 2

Graphical and numerical techniques, such as histograms and least squares lines provide identical information.

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True False

False

Q 3Q 3

The coefficient of correlation and the least squares line both describe the relationship between two interval variables.

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True False

True

Q 4Q 4

The precision provided by the numerical techniques (mean, median, and standard deviation) provides more useful information than graphical techniques (histograms and box plots) alone.

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True False

Q 5Q 5

Which of the following characteristics does a histogram help you identify?
A) The shape of distribution.
B) The approximate center of a distribution.
C) The amount of spread in a distribution.
D) All of these choices are true.

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Multiple Choice

Q 6Q 6

The shape of a distribution helps answer which question about the data?
A) Where is the approximate center of the distribution?
B) Are the observations close to one another, or are they widely dispersed?
C) Is the distribution symmetric?
D) All of these choices are true.

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Multiple Choice

Q 7Q 7

Which of the following is correct about the shape of a distribution?
A) The shape can show you how many modes there are.
B) The shape can help you determine the approximate center of the distribution.
C) The shape can help you determine whether the data are close or spread out.
D) All of these choices are true.

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Multiple Choice

Q 8Q 8

A scatter diagram reveals a strong positive linear relationship between oil and gasoline prices.Which of the following numerical techniques will not give us more detailed information about this relationship?
A) Coefficient of determination
B) Coefficient of correlation
C) Coefficient of variation.
D) All of these choices help us describe this relationship.

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Multiple Choice

Q 9Q 9

Scatter diagrams, covariance, and the coefficient of correlation are useful techniques for detecting relationships between two ____________________ variables.

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Essay

Q 10Q 10

Statisticians usually apply graphical techniques as a first step in analyzing data because we first need to know the ____________________ of the distribution.

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Q 11Q 11

Box plots and medians work well to describe ____________________ data, while histograms and means work well to describe ____________________ data.

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Q 12Q 12

____________________ techniques give you the big picture of a distribution and ____________________ techniques give you more precise details.

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Q 13Q 13

We can frequently make several inferences about the nature of the data from the ____________________ of its histogram.

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Q 14Q 14

What statistics and graphs can you use to answer the following question: Where is the approximate center of the distribution?

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Q 15Q 15

What statistics and graphs can you use to answer the following question: Are the observations close to one another, or are they widely dispersed?

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Q 16Q 16

What statistics and graphs can you use to answer the following questions: Is the distribution unimodal, bimodal, or multimodal? If there is more than one mode, where are the peaks, and where are the valleys?

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Q 17Q 17

What statistics and graphs can you use to answer the following question: Is the distribution symmetric? If not, is it skewed? If symmetric, is it bell shaped?

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Q 18Q 18

What statistics and graphs can you use to look for a relationship between two interval variables?

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Q 19Q 19

If the covariance of x and y is 26.16 and the standard deviation of x is 32.7, then the slope of the least squares line is b

_{1}=.80.Free

True False

Q 20Q 20

If , , n = 12, and the slope equals 0.5, then the y-intercept of the least squares line is b

_{0}= 276.08.Free

True False

Q 21Q 21

If the coefficient of correlation r = 0, then there can be no linear relationship between the dependent variable y and the independent variable x.

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True False

Q 22Q 22

If the coefficient of correlation r = 0, then there can be no relationship whatsoever between the dependent variable y and the independent variable x.

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True False

Q 23Q 23

If the coefficient of correlation r = .81, the standard deviations of x and y are 20 and 25, respectively, then cov(x, y) must be 405.0.

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True False

Q 24Q 24

The advantage that the coefficient of correlation has over the covariance is that the former has a set lower and upper limit.

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True False

Q 25Q 25

If the standard deviations of x and y are 12.5 and 10.8, respectively, and the covariance is 118.8, then the coefficient of correlation r is 0.88.

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True False

Q 26Q 26

Generally speaking, if two variables are unrelated, the covariance will be a number close to zero.

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True False

Q 27Q 27

Three measures of the linear relationship between x and y are the coefficient of correlation, the coefficient of determination, and the coefficient of variation.

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True False

Q 28Q 28

The coefficient of correlation r is a number that indicates the direction and the strength of the linear relationship between the dependent variable y and the independent variable x.

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True False

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True False

Q 30Q 30

A perfect straight line sloping upward would produce a correlation coefficient value of 1.0.

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True False

Q 31Q 31

When the standard deviation is expressed as a percentage of the mean, the result is the coefficient of correlation.

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True False

Q 32Q 32

If the coefficient of correlation r = 1, then the best-fit linear equation will actually include all of the observations.

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True False

Q 33Q 33

If the standard deviation of x is 18, the covariance of x and y is 120, the coefficient r = 0.90, then the standard deviation of y is 54.87.

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True False

Q 34Q 34

Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals 0.75, this means that:
A) there is very weak correlation.
B) the slope b

_{1}is = 0.75. C) the value of X is always greater than the value of Y. D) None of these choices are true.Free

Multiple Choice

Q 35Q 35

The slope b

_{1}of the least squares line represents the: A) predicted value of Y when X = 0. B) estimated average change in Y per unit change in X. C) predicted value of Y. D) variation around the regression line.Free

Multiple Choice

Q 36Q 36

Generally speaking, if two variables are unrelated (as one increases, the other shows no pattern), the covariance will be:
A) a large positive number.
B) a large negative number.
C) a positive or negative number close to zero.
D) None of these choices.

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Multiple Choice

Q 37Q 37

If the correlation coefficient r = 1.00, then all the observations must fall exactly on:
A) a straight line with a slope that equals 1.00.
B) a straight line with a negative slope.
C) a straight line with a positive slope.
D) a horizontal straight line with a zero slope.

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Multiple Choice

Q 38Q 38

The Y-intercept, b

_{0}, of the least squares line represents the: A) estimated average value of Y when X = 0. B) estimated average change in Y per unit change in X. C) predicted value of Y. D) variation around the sample regression line.Free

Multiple Choice

Q 39Q 39

A perfect straight line sloping downward would produce a correlation coefficient equal to:
A) +1.0
B) 1.0
C) 0.0
D) Cannot tell from the information given.

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Multiple Choice

Q 40Q 40

Which of the following is a property of r, the coefficient of correlation?
A) r always lies between 0 and 1.
B) r has no units.
C) If you switch the values of X and Y, the sign of r changes.
D) All of these choices are true.

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Multiple Choice

Q 41Q 41

Which of the following is a property of the slope, b

_{1}? A) The slope equals one if X and Y have the same variance. B) The slope has the same sign as r, the coefficient of correlation. C) The slope equals one if r equals one. D) All of these choices are true.Free

Multiple Choice

Q 42Q 42

Which of the following are measures of the linear relationship between two variables?
A) The covariance
B) The coefficient of correlation
C) The variance
D) Both a and b

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Multiple Choice

Q 43Q 43

The strength of the linear relationship between two interval variables can be measured by the:
A) coefficient of variation.
B) coefficient of correlation.
C) slope of the regression line.
D) Y-intercept.

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Multiple Choice

Q 44Q 44

The denominator in the calculation of the sample covariance, cov (x,y), is:
A) n 2
B) n 1
C) n
D) 2n 1

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Multiple Choice

Q 45Q 45

If cov(x, y) = 20, and then the sample coefficient of correlation r is:
A) 1.400
B) 0.026
C) 0.714
D) None of these choices.

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Multiple Choice

Q 46Q 46

The ____________________ of the correlation indicates the direction of a linear relationship.

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Q 47Q 47

The magnitude of the correlation measures the ____________________ of a linear relationship.

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Q 48Q 48

The ____________________ of a linear relationship is hard to interpret from the covariance, but it is easy to interpret from the correlation.

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Q 49Q 49

The method used to find the best fitting line through the observations is called the ____________________ method.

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Q 50Q 50

In the equation of the least squares line, , b

_{0}is the ____________________ and b_{1}is the ____________________.Free

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Q 52Q 52

The y-intercept of the least squares line is the point on the line when ________________ = 0.

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Q 53Q 53

When two variables x and y are linearly related, it does not necessarily mean that x ____________________ y.

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Q 54Q 54

The coefficient of determination is the percentage of variation in the ____________________ variable that is explained by the variation in the ____________________ variable.

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Q 55Q 55

Given the following sample data:
a.
Calculate the covariance and the correlation coefficient.
b.
Comment on the relationship between x and y.
c.
Determine the least squares line.
d.
Draw the scatter diagram and plot the least squares line.

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Q 56Q 56

Longevity and Salary
A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below:
-{Longevity and Salary Narrative}
a.
Calculate and interpret the covariance between x and y.
b.
Give a possible reason that the covariance is negative.

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Q 57Q 57

Longevity and Salary
A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below:
-{Longevity and Salary Narrative}
a.
Calculate the coefficient of correlation, and comment on the relationship between x and y.
b.
Give a possible reason that the correlation is negative.

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Q 58Q 58

Longevity and Salary
A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below:
-{Longevity and Salary Narrative} Determine the least squares line, and use it to estimate the value of y for x = 6.

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Q 59Q 59

Longevity and Salary
A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below:
-{Longevity and Salary Narrative} Draw the scatter diagram and plot the least squares line.

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Q 60Q 60

How is the value of the correlation coefficient r affected in each of the following cases?
a.
Each x value and y is multiplied by 4.
b.
Each x value is switched with the corresponding y value.
c.
Each x value is increased by 2.

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Q 61Q 61

Consider the following data:
a.
Calculate the covariance and the coefficient of correlation for the sample.
b.
What do these statistics tell you about the relationship between x and y?

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True False

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True False

Q 64Q 64

In a histogram, the proportion of the total area which must be to the left of the median is more than 0.50 if the distribution is positively skewed.

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True False

Q 65Q 65

A data sample has a mean of 107, a median of 122, and a mode of 134.The distribution of the data is positively skewed.

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True False

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True False

Q 67Q 67

In a bell shaped distribution, there is no difference in the values of the mean, median, and mode.

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True False

Q 68Q 68

Lily has been keeping track of what she spends to eat out.The last week's expenditures for meals eaten out were $5.69, $5.95, $6.19, $10.91, $7.49, $14.53, and $7.66.The mean amount Lily spends on meals is $8.35.

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True False

Q 69Q 69

In a negatively skewed distribution, the mean is smaller than the median and the median is smaller than the mode.

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True False

Q 70Q 70

The median of a set of data is more representative than the mean when the mean is larger than most of the observations.

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True False

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True False

Q 72Q 72

In a histogram, the proportion of the total area which must be to the left of the median is less than 0.50 if the distribution is negatively skewed.

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True False

Q 73Q 73

In a histogram, the proportion of the total area which must be to the right of the mean is exactly 0.50 if the distribution is symmetric and unimodal.

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True False

Q 74Q 74

Suppose a sample of size 50 has a sample mean of 20.In this case, the sum of all observations in the sample is 1,000.

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True False

Q 75Q 75

The median of an ordered data set with 30 items would be the average of the 15

^{th}and the 16^{th}observations.Free

True False

Q 76Q 76

If the mean, median, and mode are all equal, the histogram must be symmetric and bell shaped.

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True False

Q 77Q 77

Which of the following statistics is a measure of central location?
A) The mean
B) The median
C) The mode
D) All of these choices are true.

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Multiple Choice

Q 78Q 78

Which measure(s) of central location is/are meaningful when the data are ordinal?
A) The mean and median
B) The mean and mode
C) The median and mode
D) Only mean

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Multiple Choice

Q 79Q 79

Which of the following statements about the mean is not always correct?
A) The sum of the deviations from the mean is zero.
B) Half of the observations are on either side of the mean.
C) The mean is a measure of the central location.
D) The value of the mean times the number of observations equals the sum of all observations.

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Multiple Choice

Q 80Q 80

Which of the following statements is true for the following observations: 9, 8, 7, 9, 6, 11, and 13?
A) The mean, median, and mode are all equal.
B) Only the mean and median are equal.
C) Only the mean and mode are equal
D) Only the median and mode are equal.

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Multiple Choice

Q 81Q 81

In a histogram, the proportion of the total area which must be to the left of the median is:
A) exactly 0.50.
B) less than 0.50 if the distribution is negatively skewed.
C) more than 0.50 if the distribution is positively skewed.
D) unknown.

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Multiple Choice

Q 82Q 82

Which measure of central location can be used for both interval and nominal variables?
A) The mean
B) The median
C) The mode
D) All of these choices are true.

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Multiple Choice

Q 83Q 83

Which of these measures of central location is not sensitive to extreme values?
A) The mean
B) The median
C) The mode
D) All of these choices are true.

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Multiple Choice

Q 84Q 84

In a positively skewed distribution:
A) the median equals the mean.
B) the median is less than the mean.
C) the median is larger than the mean.
D) the mean can be larger or smaller than the median.

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Multiple Choice

Q 85Q 85

Which of the following statements about the median is not true?
A) It is more affected by extreme values than the mean.
B) It is a measure of central location.
C) It is equal to Q

_{2}. D) It is equal to the mode in a bell shaped distribution.Free

Multiple Choice

Q 86Q 86

Which of the following summary measures is sensitive to extreme values?
A) The median
B) The interquartile range
C) The mean
D) The first quartile

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Multiple Choice

Q 87Q 87

In a perfectly symmetric bell shaped "normal" distribution:
A) the mean equals the median.
B) the median equals the mode.
C) the mean equals the mode.
D) All of these choices are true.

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Multiple Choice

Q 88Q 88

Which of the following statements is true?
A) When the distribution is positively skewed, mean < median < mode.
B) When the distribution is negatively skewed, mean > median > mode.
C) When the distribution is symmetric and unimodal, mean = median = mode.
D) When the distribution is symmetric and bimodal, mean = median = mode.

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Multiple Choice

Q 89Q 89

In a histogram, the proportion of the total area which must be to the right of the mean is:
A) less than 0.50 if the distribution is negatively skewed.
B) exactly 0.50.
C) more than 0.50 if the distribution is positively skewed.
D) exactly 0.50 if the distribution is symmetric and unimodal.

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Multiple Choice

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Essay

Q 91Q 91

The size of a sample is denoted by the letter ____________________ and the size of a population is denoted by the letter ____________________.

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Q 92Q 92

The sample mean is denoted by ____________________ and the population mean is denoted by ____________________.

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Q 93Q 93

There are three measures of central location; the mean, the ____________________, and the ____________________.

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Q 94Q 94

The ____________________ is calculated by finding the middle of the data set, when the data are ordered from smallest to largest.

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Q 97Q 97

The ____________________ mean is used whenever we wish to find the "average" growth rate, or rate of change, in a variable over time.

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Q 98Q 98

The ____________________ mean of n returns (or growth rates) is the appropriate mean to calculate if you wish to estimate the mean rate of return (or growth rate) for any single period in the future.

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Q 99Q 99

If a data set contains an even number of observations, the median is found by taking the ____________________ of these two numbers.

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Q 101Q 101

Strip Mall Rent
Monthly rent data in dollars for a sample of 10 stores in a small town in South Dakota are as follows: 220, 216, 220, 205, 210, 240, 195, 235, 204, and 250.
-{Strip Mall Rent Narrative} Compute the sample monthly average rent.

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Q 102Q 102

Strip Mall Rent
Monthly rent data in dollars for a sample of 10 stores in a small town in South Dakota are as follows: 220, 216, 220, 205, 210, 240, 195, 235, 204, and 250.
-{Strip Mall Rent Narrative} Compute the sample median.

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Essay

Q 103Q 103

Strip Mall Rent
Monthly rent data in dollars for a sample of 10 stores in a small town in South Dakota are as follows: 220, 216, 220, 205, 210, 240, 195, 235, 204, and 250.
-{Strip Mall Rent Narrative} What is the mode?

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Essay

Q 104Q 104

Pets Survey
A sample of 36 families were asked how many pets they owned.Their responses are summarized in the following table.
-{Pets Survey Narrative} Determine the mean, the median, and the mode of the number of pets owned per family.

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Essay

Q 105Q 105

Pets Survey
A sample of 36 families were asked how many pets they owned.Their responses are summarized in the following table.
-{Pets Survey Narrative} Explain what the mean, median, and mode tell you about this particular data set.

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Essay

Q 106Q 106

How do the mean, median, and mode compare to each other when the distribution is:
a.
symmetric?
b.
negatively skewed?
c.
positively skewed?

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Q 107Q 107

A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, and 30.Compute the following measures of central location:
a.
mean
b.
median
c.
mode

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Essay

Q 108Q 108

Computers
The following data represent the number of computers owned by a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
-{Computers Narrative} Compute the mean number of computers.

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Essay

Q 109Q 109

Computers
The following data represent the number of computers owned by a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
-{Computers Narrative} Compute the median number of computers.

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Essay

Q 110Q 110

Computers
The following data represent the number of computers owned by a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
-{Computers Narrative} Is the distribution of the number of computers symmetric or skewed? Why?

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Essay

Q 111Q 111

Weights of Workers
The following data represent the number of employees of a sample of 25 companies: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Workers Narrative} Construct a stem and leaf display for the number of workers.

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Essay

Q 112Q 112

Weights of Workers
The following data represent the number of employees of a sample of 25 companies: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Workers Narrative} Find the median number of workers.

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Q 113Q 113

Weights of Workers
The following data represent the number of employees of a sample of 25 companies: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Workers Narrative} Find the mean number of workers.

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Essay

Q 114Q 114

Weights of Workers
The following data represent the number of employees of a sample of 25 companies: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Workers Narrative} Is the distribution of the number of workers symmetric or skewed? Why?

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Essay

Q 115Q 115

Weights of Workers
The following data represent the number of employees of a sample of 25 companies: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-The number of hours a college student spent studying during the final exam week was recorded as follows: 7,6, 4, 9, 8, 5, and 10.Compute for the data and the value in an appropriate unit.

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Essay

Q 116Q 116

Hours Worked per Week
The following data represent the hours worked per week of a sample of 25 employees from a government department: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Hours Worked per Week Narrative} Construct a stem and leaf display for the hours.

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Essay

Q 117Q 117

Hours Worked per Week
The following data represent the hours worked per week of a sample of 25 employees from a government department: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Hours Worked per Week Narrative} Find the median hours.

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Q 118Q 118

Hours Worked per Week
The following data represent the hours worked per week of a sample of 25 employees from a government department: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Hours Worked per Week Narrative} Compute the sample mean hours.

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Q 119Q 119

Hours Worked per Week
The following data represent the hours worked per week of a sample of 25 employees from a government department: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Hours Worked per Week Narrative} Find the modal hours.

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Q 120Q 120

Hours Worked per Week
The following data represent the hours worked per week of a sample of 25 employees from a government department: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Hours Worked per Week Narrative} Compare the mean and median hours for these employees and use them to discuss the shape of the distribution.

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Essay

Q 121Q 121

Salaries of Employees
The following data represent the yearly salaries (in thousands of dollars) of a sample of 13 employees of a firm: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
-{Salaries of Employees Narrative} Compute the mean salary.

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Q 122Q 122

Salaries of Employees
The following data represent the yearly salaries (in thousands of dollars) of a sample of 13 employees of a firm: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
-{Salaries of Employees Narrative} Compute the median salary.

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Essay

Q 123Q 123

Salaries of Employees
The following data represent the yearly salaries (in thousands of dollars) of a sample of 13 employees of a firm: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
-{Salaries of Employees Narrative} Compare the mean salary with the median salary and use them to describe the shape of the distribution.

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Essay

Q 124Q 124

A sample of 12 construction workers has a mean age of 25 years.Suppose that the sample is enlarged to 14 construction workers, by including two additional workers having common age of 25 each.Find the mean of the sample of 14 workers.

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Q 125Q 125

The mean of a sample of 15 measurements is 35.6 feet.Suppose that the sample is enlarged to 16 measurements, by including one additional measurement having a value of 42 feet.Find the mean of the sample of the 16 measurements.

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Q 126Q 126

A mutual fund you purchased in the years 2011-2014 has the following rates of return shown below:
Compute the geometric mean.

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Q 127Q 127

2-Year Investment
Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year, however, the investment suffers a 50% loss, from $10,000 back to $5,000.
-{2-Year Investment Narrative} Calculate the arithmetic mean.

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Essay

Q 128Q 128

2-Year Investment
Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year, however, the investment suffers a 50% loss, from $10,000 back to $5,000.
-{2-Year Investment Narrative} Calculate the geometric mean.

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Essay

Q 129Q 129

2-Year Investment
Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year, however, the investment suffers a 50% loss, from $10,000 back to $5,000.
-{2-Year Investment Narrative} Compare the values of the arithmetic and geometric means.

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Essay

Q 130Q 130

Ages of Senior Citizens
A sociologist recently conducted a survey of citizens over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 22 uninsured senior citizens were as follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 86, 87, 91, 92, 94, and 97.
-{Ages of Senior Citizens Narrative} Calculate the mean age of the uninsured senior citizens

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Essay

Q 131Q 131

Ages of Senior Citizens
A sociologist recently conducted a survey of citizens over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 22 uninsured senior citizens were as follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 86, 87, 91, 92, 94, and 97.
-{Ages of Senior Citizens Narrative} Calculate the median age of the uninsured senior citizens.

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Essay

Q 132Q 132

Ages of Senior Citizens
A sociologist recently conducted a survey of citizens over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 22 uninsured senior citizens were as follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 86, 87, 91, 92, 94, and 97.
-{Ages of Senior Citizens Narrative} Explain why there is no mode for this data set.

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Essay

Q 133Q 133

Suppose that a firm's sales were $2,500,000 four years ago, and sales have grown annually by 25%, 15%, 5%, and 10% since that time.What was the geometric mean growth rate in sales over the past four years?

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Essay

Q 134Q 134

Suppose that a firm's sales were $3,750,000 five years ago and are $5,250,000 today.What was the geometric mean growth rate in sales over the past five years?

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Essay

Q 135Q 135

The value of the standard deviation may be either positive or negative, while the value of the variance will always be positive.

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True False

Q 136Q 136

The difference between the largest and smallest observations in an ordered data set is called the range.

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True False

Q 137Q 137

The standard deviation is expressed in terms of the original units of measurement but the variance is not.

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True False

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True False

Q 139Q 139

While Chebysheff's Theorem applies to any distribution, regardless of shape, the Empirical Rule applies only to distributions that are bell shaped.

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True False

Q 140Q 140

The mean of fifty sales receipts is $65.75 and the standard deviation is $10.55.Using Chebysheff's Theorem, 75% of the sales receipts were between $44.65 and $86.85.

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True False

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True False

Q 142Q 142

According to Chebysheff's Theorem, at least 93.75% of observations should fall within 4 standard deviations of the mean.

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True False

Q 143Q 143

Chebysheff's Theorem states that the percentage of observations in a data set that should fall within five standard deviations of their mean is at least 96%.

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True False

Q 144Q 144

The Empirical Rule states that the percentage of observations in a data set (providing that the data set is bell shaped) that fall within one standard deviation of their mean is approximately 75%.

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True False

Q 145Q 145

A population with 200 elements has a variance of 20.From this information, it can be shown that the population standard deviation is 10.

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True False

Q 146Q 146

If two data sets have the same range, the distances from the smallest to largest observations in both sets will be the same.

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True False

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True False

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True False

Q 149Q 149

If two data sets have the same standard deviation, they must have the same coefficient of variation.

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True False

Q 150Q 150

The units for the variance are the same as the units for the original data (for example, feet, inches, etc.).

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True False

Q 151Q 151

The units for the standard deviation are the same as the units for the original data (for example, feet, inches, etc.).

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True False

Q 152Q 152

The variance is more meaningful and easier to interpret compared to the standard deviation.

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True False

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True False

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True False

Q 155Q 155

The coefficient of variation allows us to compare two sets of data based on different measurement units.

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True False

Q 156Q 156

If the observations are in the millions, a standard deviation of 10 would be considered small.If the observations are all less than 50, a standard deviation of 10 would be considered large.

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True False

Q 157Q 157

If two data sets have the same range:
A) the distances from the smallest to largest observations in both sets will be the same.
B) the smallest and largest observations are the same in both sets.
C) both sets will have the same standard deviation.
D) both sets will have the same interquartile range.

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Multiple Choice

Q 158Q 158

The Empirical Rule states that the approximate percentage of measurements in a data set (providing that the data set has a bell shaped distribution) that fall within two standard deviations of their mean is approximately:
A) 68%.
B) 75%.
C) 95%.
D) 99%.

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Multiple Choice

Q 159Q 159

Which of the following summary measures is affected most by extreme values?
A) The median.
B) The mean.
C) The range.
D) The interquartile range.

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Multiple Choice

Q 160Q 160

Chebysheff's Theorem states that the percentage of measurements in a data set that fall within three standard deviations of their mean is:
A) 75%.
B) at least 75%.
C) 89%.
D) at least 88.9%.

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Multiple Choice

Q 161Q 161

Which of the following is a measure of variability?
A) The interquartile range.
B) The variance.
C) The coefficient of variation.
D) All of these choices are true.

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Multiple Choice

Q 162Q 162

The smaller the spread of scores around the mean:
A) the smaller the variance of the data set.
B) the smaller the standard deviation of the data set.
C) the smaller the coefficient of variation of the data set.
D) All of these choices are true.

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Multiple Choice

Q 163Q 163

Is a standard deviation of 10 a large number indicating great variability, or is it small number indicating little variability? To answer this question correctly, one should look carefully at the value of the:
A) mean.
B) standard deviation.
C) coefficient of variation.
D) mean dividing by the standard deviation.

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Multiple Choice

Q 164Q 164

Which of the following types of data has no measure of variability?
A) Interval data.
B) Nominal data.
C) Bimodal data.
D) None of these choices.

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Multiple Choice

Q 165Q 165

Which of the following statements is true regarding the data set 8, 8, 8, 8, and 8?
A) The range equals 0.
B) The standard deviation equals 0.
C) The coefficient of variation equals 0.
D) All of these choices are true.

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Multiple Choice

Q 166Q 166

According to the Empirical Rule, if the data form a bell shaped normal distribution, approximately ____________________ percent of the observations will be contained within 2 standard deviations around the mean.

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Essay

Q 167Q 167

According to the Empirical Rule, if the data form a bell shaped normal distribution approximately ____________________ percent of the observations will be contained within 1 standard deviation around the mean.

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Essay

Q 168Q 168

According to the Empirical Rule, if the data form a bell shaped normal distribution approximately ____________________ percent of the observations will be contained within 3 standard deviations around the mean.

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Essay

Q 169Q 169

There are three statistics used to measure variability in a data set; the range, the ____________________, and the ____________________.

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Essay

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Essay

Q 172Q 172

The ____________________ uses both the mean and the standard deviation to interpret standard deviation for bell shaped histograms.

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Essay

Q 173Q 173

____________________ uses both the mean and the standard deviation to interpret standard deviation for histograms of any shape.

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Essay

Q 174Q 174

A statistic that interprets the standard deviation relative to the size of the numbers in the data set is called the ____________________ of ____________________.

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Essay

Q 175Q 175

The range, variance, standard deviation, and coefficient of variation are to be used only on ____________________ data.

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Essay

Q 176Q 176

A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, and 30.Compute the following measures of variability.
a.
Standard deviation
b.
Coefficient of variation
c.
Compare the standard deviation and coefficient of variation and use them to discuss the variability in the data.

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Essay

Q 177Q 177

The following data represent the number of children in a sample of 10 families from a certain community: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
a.
Compute the range.
b.
Compute the variance.
c.
Compute the standard deviation.
d.
Compute the coefficient of variation.
e.
Explain why in this case range > variance > standard deviation > coefficient of variation.

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Essay

Q 178Q 178

Weights of Teachers
The following data represent the weights in pounds of a sample of 25 teachers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Teachers Narrative} Compute the sample variance and sample standard deviation.

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Essay

Q 179Q 179

Weights of Teachers
The following data represent the weights in pounds of a sample of 25 teachers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Teachers Narrative} Compute the range and coefficient of variation.

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Essay

Q 180Q 180

Weights of Teachers
The following data represent the weights in pounds of a sample of 25 teachers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Teachers Narrative} Which is a better measure of variability in the weights of the teachers, the standard deviation or the coefficient of variation?

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Essay

Q 181Q 181

Is it possible for the standard deviation of a data set to be larger than its variance? Explain.

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Essay

Q 182Q 182

Ages of Workers
The ages (in years) of three groups of workers are shown below:
-{Ages of Workers Narrative} Calculate and compare the standard deviations for the three samples.

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Essay

Q 183Q 183

Ages of Workers
The ages (in years) of three groups of workers are shown below:
-{Ages of Workers Narrative} Compute and compare the ranges for the three groups.

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Essay

Q 184Q 184

Ages of Workers
The ages (in years) of three groups of workers are shown below:
-{Ages of Workers Narrative} Compute and compare the coefficient of variation for the three samples.

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Essay

Q 185Q 185

Suppose your data set contains ages (in years) and you calculate the range, variance, standard deviation, and coefficient of variation for the data.Explain what units each of these measures is in.

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Essay

Q 186Q 186

The number of hours a college student spent studying during the final exam week was recorded as follows: 6, 5, 2, 8, 7, 4, and 9.Compute the range for the data, express the number in the appropriate unit.

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Essay

Q 187Q 187

The number of hours a college student spent studying during the final exam week was recorded as follows: 7, 6, 4, 9, 8, 5, and 10.Compute s

^{2}and s for the data and express the numbers in the appropriate unit.Free

Essay

Q 188Q 188

The annual percentage rates of return over the past 10 years for two mutual funds are as shown below.Which fund would you classify as having the higher level of risk?

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Essay

Q 189Q 189

Ages of Volunteers
The following data represent the ages in years of a sample of 25 volunteers from a charitable organization: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Ages of Volunteers Narrative} Compute the range of the data and express the number in the appropriate unit.

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Essay

Q 190Q 190

Ages of Volunteers
The following data represent the ages in years of a sample of 25 volunteers from a charitable organization: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Ages of Volunteers Narrative} Compute the sample variance and sample standard deviation, and express the numbers in the appropriate units.

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Essay

Q 191Q 191

Ages of Volunteers
The following data represent the ages in years of a sample of 25 volunteers from a charitable organization: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Ages of Volunteers Narrative} Compute the coefficient of variation and express the number in the appropriate unit.

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Essay

Q 192Q 192

Salaries of Office Workers
The following data represent the salaries (in thousands of dollars) of a sample of 13 office workers of a firm: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
-{Salaries of Office Workers Narrative} Compute the variance and standard deviation of the salaries, and express the numbers in the appropriate units.

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Essay

Q 193Q 193

Salaries of Office Workers
The following data represent the salaries (in thousands of dollars) of a sample of 13 office workers of a firm: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
-{Salaries of Office Workers Narrative} Compute the coefficient of variation and express the number in the appropriate unit.

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Essay

Q 194Q 194

Salaries of Office Workers
The following data represent the salaries (in thousands of dollars) of a sample of 13 office workers of a firm: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
-{Salaries of Office Workers Narrative} Compute the range.

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Essay

Q 195Q 195

Consider the following population of measurements: 162, 152, 177, 157, 184, 176, 165, 181, 170, and 163.Label and compute the variance and standard deviation.

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Essay

Q 196Q 196

Milk Demand
A supermarket has determined that daily demand for milk containers has an approximate bell shaped distribution, with a mean of 55 containers and a standard deviation of six containers.
-{Milk Demand Narrative} How often can we expect between 49 and 61 containers to be sold in a day? (Give a percentage.)

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Essay

Q 197Q 197

Milk Demand
A supermarket has determined that daily demand for milk containers has an approximate bell shaped distribution, with a mean of 55 containers and a standard deviation of six containers.
-{Milk Demand Narrative} What percentage of the time will the number of containers of milk sold be more than 2 standard deviations from the mean?

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Essay

Q 198Q 198

Milk Demand
A supermarket has determined that daily demand for milk containers has an approximate bell shaped distribution, with a mean of 55 containers and a standard deviation of six containers.
-{Milk Demand Narrative} If the supermarket begins each morning with a supply of 67 containers of milk, how often will demand exceed the supply? (Give a percentage.)

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Essay

Q 199Q 199

A sample of 13 college professors has a mean age of 30 years and a standard deviation of 5 years.Suppose that the sample is enlarged to 15 college professors, by including two additional professors that are each 30 years old.Will the standard deviation increase, decrease, or stay the same, and why?

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Essay

Q 200Q 200

The price-earnings ratios of a sample of stocks have a mean value of 13.5 and a standard deviation of 2.If the ratios have a bell shaped distribution, what can we say about the proportion of ratios that fall between
a.
11.5 and 15.5?
b.
9.5 and 17.5?
c.
7.5 and 19.5?

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Essay

Q 201Q 201

The distance between the 25th percentile and the median is always the same as the distance between the median and the 75th percentile.

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True False

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True False

Q 203Q 203

The interquartile range is found by taking the difference between the 1st and 3rd quartiles and dividing that value by 2.

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True False

Q 204Q 204

Quartiles divide the observations in a data set into four parts with the same amount of data in each part.

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True False

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True False

Q 206Q 206

Expressed in percentiles, the interquartile range is the difference between the 25th and 75th percentiles.

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True False

Q 207Q 207

If the distribution of a data set were perfectly symmetric, the distance from Q

_{1}to the median would always equal the distance from Q_{3}to the median in a box plot.Free

True False

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True False

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True False

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True False

Q 211Q 211

Percentiles can be converted into quintiles and deciles, where quintiles divide the data into fifths, and deciles divide the data into tenths.

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True False

Q 212Q 212

The 5-number summary consists of the smallest observation, the first quartile, the median, the third quartile, and the largest observation.

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True False

Q 213Q 213

In a negatively skewed distribution, the distance from the smallest observation to Q

_{1}exceeds the distance from Q_{3}to the largest observation.Free

True False

Free

True False

Q 215Q 215

In a positively skewed distribution, the percentage of data between the smallest observation and Q

_{1}is less than the percentage of data between Q_{3}and the largest observation.Free

True False

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True False

Free

True False

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True False

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True False

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True False

Q 221Q 221

When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriate?
A) Coefficient of variation and range
B) Mean and standard deviation
C) Interquartile range and median
D) Variance and interquartile range

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Multiple Choice

Q 222Q 222

The length of the box in the box plot portrays the:
A) median.
B) interquartile range.
C) range.
D) third quartile.

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Multiple Choice

Q 223Q 223

In a negatively skewed distribution, which of the following is the correct statement?
A) The distance from Q

_{1}to Q_{2}is smaller than the distance from Q_{2}to Q_{3}. B) The distance from Q_{1}to Q_{2}is larger than the distance from Q_{2}to Q_{3}. C) The distance from Q_{1}to Q_{2}is half the distance from Q_{2}to Q_{3}. D) The distance from Q_{1}to Q_{3}is twice the distance from the Q_{1}to Q_{2}.Free

Multiple Choice

Q 224Q 224

In a perfectly symmetric distribution, which of the following statements is false?
A) The distance from Q

_{1}to Q_{2}equals to the distance from Q_{2}to Q_{3}. B) The distance from the smallest observation to Q_{1}is the same as the distance from Q_{3}to the largest observation. C) The distance from the smallest observation to Q_{2}is the same as the distance from Q_{2}to the largest observation. D) The distance from Q_{1}to Q_{3}is half of the distance from the smallest to the largest observation.Free

Multiple Choice

Q 225Q 225

Which of the following summary measures cannot be easily approximated from a box plot?
A) The range
B) The interquartile range
C) The second quartile
D) The standard deviation

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Multiple Choice

Q 226Q 226

The interquartile range is the difference between the:
A) largest and smallest numbers in the data set.
B) 25th percentile and the 75th percentile.
C) median and the mean.
D) None of these choices.

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Multiple Choice

Q 227Q 227

In a positively skewed distribution, which of the following is the correct statement?
A) The distance from Q

_{1}to Q_{2}is larger than the distance from Q_{2}to Q_{3}. B) The distance from Q_{1}to Q_{2}is smaller than the distance from Q_{2}to Q_{3}. C) The distance from Q_{1}to Q_{2}is twice the distance from Q_{2}to Q_{3.}D) The distance from Q_{1}to Q_{2}is half the distance from Q_{2}to Q_{3}.Free

Multiple Choice

Q 228Q 228

Which measures of central location and variability are considered to be resistant to extreme values?
A) The mean and standard deviation.
B) The mode and variance.
C) The median and interquartile range.
D) None of these choices.

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Multiple Choice

Q 229Q 229

Which of the following measures of variability is not sensitive to extreme values?
A) The range
B) The standard deviation
C) The interquartile range
D) The coefficient of variation

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Multiple Choice

Q 230Q 230

Which of the following statements is true?
A) The lower or first quartile is labeled Q

_{1}and is equal to the 25^{th}percentile. B) The second quartile is labeled Q_{2}and is equal to the median. C) The upper or third quartile is labeled Q_{3}and is equal to the 75^{th}percentile. D) All of these choices are true.Free

Multiple Choice

Q 231Q 231

If the first and second quartiles are closer to each other than are the second and third quartiles, then the shape of the histogram based on the quartiles is ____________________.

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Essay

Q 232Q 232

If the first and second quartiles are farther apart than the second and third quartiles, then the shape of the histogram based on the quartiles is ____________________.

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Essay

Free

Essay

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Essay

Q 235Q 235

The horizontal lines extending to the left and to the right of the box in a box plot are called ____________________.

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Essay

Free

Essay

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Essay

Q 238Q 238

The 10th ____________________ is the value for which 10% of the observations are less than that value.

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Essay

Free

Essay

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Essay

Q 241Q 241

Weights of Police Officers
The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Police Officers Narrative} Determine the location and value of the lower quartile of the weights.

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Essay

Q 242Q 242

Weights of Police Officers
The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Police Officers Narrative} Determine the location and value of the second quartile of the weights.

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Essay

Q 243Q 243

Weights of Police Officers
The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Police Officers Narrative} Determine the location and value of the upper quartile of the weights.

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Essay

Q 244Q 244

Weights of Police Officers
The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Police Officers Narrative} Describe the shape of the distribution of weights based on the quartiles' values.

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Essay

Q 245Q 245

Weights of Police Officers
The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Police Officers Narrative} Determine the location and value of the 60th percentile of the weights.

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Essay

Q 246Q 246

Weights of Police Officers
The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Police Officers Narrative} Construct a frequency distribution for the data, using five class intervals, and the value 130 as the lower limit of the first class.

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Essay

Q 247Q 247

Weights of Police Officers
The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Police Officers Narrative} Construct a relative frequency histogram for the data, using five class intervals and the value 130 as the lower limit of the first class.

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Essay

Q 248Q 248

Weights of Police Officers
The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Police Officers Narrative} What does the histogram tell you about the distribution of the weights of workers?

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Essay

Q 249Q 249

Weights of Police Officers
The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Police Officers Narrative}
a.
Construct a box plot for the weights.
b.
Are there any extreme values?
c.
What does the box plot tell you about the distribution of the data?

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Essay

Q 250Q 250

Weights of Police Officers
The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Police Officers Narrative} Calculate the 3rd and 7th deciles of the data.

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Essay

Q 251Q 251

Hours of Playing Video Games
Suppose that the following data provide the hours of playing video games per week for a sample of 15 high school students in Roanoke, Virginia: 5, 11, 25, 19, 18, 20, 27, 13, 8, 10, 15, 19, 18, 9, and 12.
-{Hours of Playing Video Games Narrative} Determine the location and value of the first quartile.

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Essay

Q 252Q 252

Hours of Playing Video Games
Suppose that the following data provide the hours of playing video games per week for a sample of 15 high school students in Roanoke, Virginia: 5, 11, 25, 19, 18, 20, 27, 13, 8, 10, 15, 19, 18, 9, and 12.
-{Hours of Playing Video Games Narrative} Determine the location and value of the second quartile.

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Essay

Q 253Q 253

Hours of Playing Video Games
Suppose that the following data provide the hours of playing video games per week for a sample of 15 high school students in Roanoke, Virginia: 5, 11, 25, 19, 18, 20, 27, 13, 8, 10, 15, 19, 18, 9, and 12.
-{Hours of Playing Video Games Narrative} Determine the location and value of the third quartile.

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Essay

Q 254Q 254

Hours of Playing Video Games
Suppose that the following data provide the hours of playing video games per week for a sample of 15 high school students in Roanoke, Virginia: 5, 11, 25, 19, 18, 20, 27, 13, 8, 10, 15, 19, 18, 9, and 12.
-{Hours of Playing Video Games Narrative} Calculate and interpret the interquartile range.

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Essay

Q 255Q 255

Ages of Jockeys
The following data represent the ages in years of a sample of 25 jockeys from a local race track: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Ages of Jockeys Narrative} Find the lower quartile of the ages.

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Essay

Q 256Q 256

Ages of Jockeys
The following data represent the ages in years of a sample of 25 jockeys from a local race track: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Ages of Jockeys Narrative} Find the upper quartile of the ages.

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Essay

Q 257Q 257

Ages of Jockeys
The following data represent the ages in years of a sample of 25 jockeys from a local race track: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Ages of Jockeys Narrative} Compute the interquartile range of the data and interpret its meaning.

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Essay

Q 258Q 258

Ages of Jockeys
The following data represent the ages in years of a sample of 25 jockeys from a local race track: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Ages of Jockeys Narrative}
a.
Construct a box plot for the ages and identify any extreme values.
b.
What does the box plot tell you about the distribution of the data?

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Essay

Q 259Q 259

Ages of Jockeys
The following data represent the ages in years of a sample of 25 jockeys from a local race track: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Ages of Jockeys Narrative} Construct a relative frequency distribution for the data, using five class intervals and the value 20 as the lower limit of the first class.

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Essay

Q 260Q 260

Ages of Jockeys
The following data represent the ages in years of a sample of 25 jockeys from a local race track: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20.
-{Ages of Jockeys Narrative}
a.
Construct a relative frequency histogram for the data.
b.
What does the histogram tell you about the distribution of the data?

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Q 261Q 261

Yearly Donations
The following data represent the yearly donations (in thousands of dollars) of a sample of 13 benefactors: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
-{Yearly Donations Narrative} Compute the lower quartile for the donations.

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Q 262Q 262

Yearly Donations
The following data represent the yearly donations (in thousands of dollars) of a sample of 13 benefactors: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
-{Yearly Donations Narrative} Compute median.

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Q 263Q 263

Yearly Donations
The following data represent the yearly donations (in thousands of dollars) of a sample of 13 benefactors: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
-{Yearly Donations Narrative} Compute the upper quartile.

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Q 264Q 264

Yearly Donations
The following data represent the yearly donations (in thousands of dollars) of a sample of 13 benefactors: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
-{Yearly Donations Narrative}
a.
Describe the shape of distribution of donations based on the values of the quartiles.
b.
Give a possible reason for the shape of this data set, in terms of donations.

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Q 265Q 265

Yearly Donations
The following data represent the yearly donations (in thousands of dollars) of a sample of 13 benefactors: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
-{Yearly Donations Narrative} Compute and interpret the 90th percentile.

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Q 266Q 266

Test Scores
Suppose that an analysis of a set of test scores reveals that: Q

_{1}= 45, Q_{2}= 85, Q_{3}= 105. -{Test Scores Narrative} What do these statistics tell you about the shape of the distribution of test scores?Free

Essay

Q 267Q 267

Test Scores
Suppose that an analysis of a set of test scores reveals that: Q

_{1}= 45, Q_{2}= 85, Q_{3}= 105. -{Test Scores Narrative} What can you say about the relative position of each of the observations 34, 84, and 104, within this data set?Free

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Q 268Q 268

Test Scores
Suppose that an analysis of a set of test scores reveals that: Q

_{1}= 45, Q_{2}= 85, Q_{3}= 105. -{Test Scores Narrative} Calculate the interquartile range.What does this tell you about the data?Free

Essay

Q 269Q 269

Ages of Retirees
A sociologist recently conducted a survey of retirees over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 20 uninsured retirees were as follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 78, 79, 80, 81, 86, 87, 91, 92, 94, and 97.
-{Ages of Retirees Narrative} Calculate the first quartile of the ages of the uninsured retirees.

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Q 270Q 270

Ages of Retirees
A sociologist recently conducted a survey of retirees over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 20 uninsured retirees were as follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 78, 79, 80, 81, 86, 87, 91, 92, 94, and 97.
-{Ages of Retirees Narrative} Calculate the third quartile of the ages of the uninsured retirees.

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Q 271Q 271

Ages of Retirees
A sociologist recently conducted a survey of retirees over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 20 uninsured retirees were as follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 78, 79, 80, 81, 86, 87, 91, 92, 94, and 97.
-{Ages of Retirees Narrative} Identify the interquartile range of the ages of the uninsured retirees.What does this value tell you about the data?

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Q 272Q 272

Ages of Retirees
A sociologist recently conducted a survey of retirees over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 20 uninsured retirees were as follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 78, 79, 80, 81, 86, 87, 91, 92, 94, and 97.
-{Ages of Retirees Narrative} What does the value of the first quartile tell you?

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Q 273Q 273

Ages of Retirees
A sociologist recently conducted a survey of retirees over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 20 uninsured retirees were as follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 78, 79, 80, 81, 86, 87, 91, 92, 94, and 97.
-{Ages of Retirees Narrative} What does the value of the third quartile tell you?

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Q 274Q 274

Ages of Retirees
A sociologist recently conducted a survey of retirees over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 20 uninsured retirees were as follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 78, 79, 80, 81, 86, 87, 91, 92, 94, and 97.
-{Ages of Retirees Narrative} Describe the shape of the distribution of ages by comparing the quartiles.

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