Deck 4: Numerical Descriptive Techniques

Question 1

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

Answer 1

shape

Question 2

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

Answer 2

skewed; symmetric

Question 3

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 b₁ =.80.

Answer 3

False

Question 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.

Question 5

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?

Question 6

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.

Question 7

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

Question 8

If , , n = 12, and the slope equals 0.5, then the y-intercept of the least squares line is b₀ = 276.08.

Question 9

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

Question 10

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.

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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?

Question 16

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

Question 17

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.

Question 18

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

Question 19

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.

Question 20

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

Question 21

The variance is a measure of the linear relationship between two variables.

Question 22

The slope b₁ 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.

Question 23

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.

Question 24

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

Question 25

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.

Question 26

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.

Question 27

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.

Question 28

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.

Question 29

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

Question 30

The Y-intercept, b₀, 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.

Question 31

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

Question 32

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 b₁ is = -0.75.
C) the value of X is always greater than the value of Y.
D) None of these choices are true.

Question 33

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

Question 34

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

Question 35

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.

Question 36

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

Question 37

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

Question 38

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.

Question 39

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.

Question 40

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

Question 41

In the equation of the least squares line, , b₀ is the ____________________ and b₁ is the ____________________.

Question 42

The ____________________ measures the margin of relative change in the dependent variable.

Question 43

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.

Question 44

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.

Question 45

The denominator in the calculation of the sample covariance, cov (x,y), is:

A) n-2
B) n - 1
C) n
D) 2n- 1

Question 46

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

Question 47

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.

Question 48

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.

Question 49

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

Question 50

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.

Question 51

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

Question 52

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

Question 53

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.

Question 54

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

Question 55

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

Question 56

Which of the following is a property of the slope, b₁?

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.

Question 57

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

Question 58

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.

Question 59

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

Question 60

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.

Question 61

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.

Question 62

$\mu$ is a population parameter and is a sample statistic.

Question 63

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.

Question 64

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?

Question 65

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.

Question 66

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.

Question 67

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

Question 68

The median of an ordered data set with 30 items would be the average of the 15^th and the 16^th observations.

Question 69

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

Question 70

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.

Question 71

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

Question 72

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

Question 73

The value of the mean times the number of observations equals the sum of the observations.

Question 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.

Question 75

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.

Question 76

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.

Question 77

The mean is a measure of variability.

Question 78

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.

Question 79

The mean is affected by extreme values but the median is not.

Question 80

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