Deck 4: Numerical Descriptive Techniques

Question 1

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.

Answer 1

All of these choices are true.

Question 2

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

Answer 2

shape

Question 3

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

Answer 3

True

Question 4

If $\sum x _ { i } = 7587$ , $\sum y _ { i } = 7106.4$ , n = 12, and the slope equals 0.5, then the y-intercept of the least squares line is b₀ = 276.08.

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

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

Question 7

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.

Question 8

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 9

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 10

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

Question 11

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

Question 12

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 13

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

Question 14

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 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?

Question 16

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

Question 17

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

Question 18

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 19

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

Question 20

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

Question 21

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 22

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 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

The slope b₁ of the least squares line $\tilde { y } = b _ { 0 } + b _ { 1 } x$ 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 25

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 26

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 27

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

Question 28

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

Question 29

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

Question 30

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 31

The Y-intercept, b₀, of the least squares line $\tilde { y } = b _ { 0 } + b _ { 1 } x$ 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 32

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 33

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 34

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

Question 35

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

Question 36

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

Question 37

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

Question 38

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 39

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 40

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

Question 41

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

Question 42

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

Question 43

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

Question 44

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 45

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 46

NARRBEGIN: Experience and Salary
Longevity and Salary
A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below:
NARREND
{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 47

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

Question 48

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

Question 49

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 50

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

Question 51

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 52

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

Question 53

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

Question 54

NARRBEGIN: Experience and Salary
Longevity and Salary
A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below:
NARREND
{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 55

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

Question 56

If cov(x, y) = 20, $s _ { x } ^ { 2 } = 16$ and $s _ { y } ^ { 2 } = 49$ then the sample coefficient of correlation r is:

A)1.400
B)0.026
C)0.710
D)None of these choices.

Question 57

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

Question 58

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 59

NARRBEGIN: Experience and Salary
Longevity and Salary
A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below:
NARREND
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 60

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

Question 61

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

Question 62

The value for Q₃ can never be smaller than the value for Q₁.

Question 63

The first and second quartiles of a data set can never be equal.

Question 64

The interquartile range is an interval of numbers starting at Q₁ and ending at Q₃.

Question 65

The line drawn within the box of a box plot always represents the mean.

Question 66

The interquartile range will always exceed that of the range.

Question 67

A box plot is a graphical representation of the 5-number summary.

Question 68

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

Question 69

NARRBEGIN: Experience and Salary
Longevity and Salary
A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below:
NARREND
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 70

The line drawn within the box of a box plot always represents the median.

Question 71

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

Question 72

In a negatively skewed distribution, the distance from the smallest observation to Q₁ exceeds the distance from Q₃ to the largest observation.

Question 73

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

Question 74

The interquartile range is a measure of variability in a set of data.

Question 75

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

Question 76

In symmetric data, the value for Q₂ is always halfway between Q₁ and Q₃.

Question 77

In a positively skewed distribution, the percentage of data between the smallest observation and Q₁ is less than the percentage of data between Q₃ and the largest observation.

Question 78

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

Question 79

If the distribution of a data set were perfectly symmetric, the distance from Q₁ to the median would always equal the distance from Q₃ to the median in a box plot.

Question 80

The length of the box in a box plot portrays the interquartile range.