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.

Accepted Answer

All of these choices are true. 
The shape of a distribution can show you how many modes there are, which helps in identifying any potential outliers. The shape also helps in determining the approximate center of the distribution, which is important when describing the data. Additionally, the shape can help in determining whether the data are close or spread out, which tells us about the variability of the data.

Question 2

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

Accepted Answer

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.

Accepted Answer

Graphical techniques such as histograms or box plots can help us visualize the distribution and identify any potential outliers or patterns. This information is important in selecting appropriate statistical methods and interpreting the results.

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.

Accepted Answer

The y-intercept of the least squares line is calculated as b0 = ȳ - b1x̄, where ȳ is the mean of the y-values, x̄ is the mean of the x-values, and b1 is the slope. In this case, ȳ = 7106.4/12 = 592.2, x̄ = 7587/12 = 632.25, and b1 = 0.5. Therefore, b0 = 592.2 - 0.5(632.25) = 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?

Accepted Answer

The answer of What statistics and graphs can you use...

Question 6

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

Accepted Answer

Both the coefficient of correlation and the least squares line are used to describe the relationship between two interval variables. The coefficient of correlation measures the strength and direction of the linear relationship between the variables, while the least squares line represents a linear model that predicts the value of one variable based on the value of the other variable.

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.

Accepted Answer

The slope of the least squares line ($b$) is calculated using the formula $b = \frac{\text{Covariance of } x \text{ and } y}{\text{Variance of } x}$. Given the covariance of $x$ and $y$ is 26.16 and the standard deviation of $x$ is 32.7, the variance of $x$ would be $32.7^2$. The provided slope value does not match the calculation based on these inputs.

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?

Accepted Answer

The answer of What statistics and graphs can you use...

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.

Accepted Answer

Coefficient of variation is a measure of relative variability and does not provide information about the relationship between two variables. The other two options, coefficient of determination and coefficient of correlation, are both measures of the strength and direction of a linear relationship between two variables and would provide more detailed information about the relationship between oil and gasoline prices.

Question 10

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

Accepted Answer

The answer of What statistics and graphs can you use...

Question 11

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

Accepted Answer

The answer of We can frequently make several inferences about...

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.

Accepted Answer

The answer of The precision provided by the numerical techniques...

Question 13

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

Accepted Answer

The answer of Box plots and medians work well to...

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.

Accepted Answer

A histogram can help identify the shape of distribution, the approximate center of a distribution, and the amount of spread in a distribution. Therefore, 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?

Accepted Answer

The answer of What statistics and graphs can you use...

Question 16

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

Accepted Answer

Graphical and numerical techniques provide different types of information. Histograms provide a visual representation of the distribution of data, while least squares lines provide a numerical estimation of the relationship between two variables. While both can be used to analyze data, they do not 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?

Accepted Answer

The answer of What statistics and graphs can you use...

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.

Accepted Answer

The shape of a distribution can provide information about the center, spread, and symmetry of the data, so all of the choices listed are true.

Question 19

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

Accepted Answer

The answer of Scatter diagrams, covariance, and the coefficient of...

Question 20

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

Accepted Answer

The answer of ____________________ techniques give you the big picture...

Quiz 4: Numerical Descriptive Techniques

Which of the following is correct about the shape of a distribution?

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

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

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.

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?

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

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.

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?

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?

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

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

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

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

Which of the following characteristics does a histogram help you identify?

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

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

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

The shape of a distribution helps answer which question about the data?

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

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

Quiz 4: Numerical Descriptive Techniques

Which of the following is correct about the shape of a distribution?

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

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

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

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?

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

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.

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?

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?

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

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

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

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

Which of the following characteristics does a histogram help you identify?

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

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

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

The shape of a distribution helps answer which question about the data?

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

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

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.

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.

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

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