Deck 3: Summary Statistics

Question 1

Suppose that a data set contains 275 observations ranging from a low of 6,000 to a high of 70,000.What is the appropriate class width to use when constructing a histogram for the data?

A)6,400
B)7,112
C)7,778
D)8,000

Answer 1

B

Question 2

The standard deviation of a distribution provides a sense of

A)how far data points tend to fall from the median.
B)where the central mass of the distribution lies.
C)how far data points tend to fall from the mean.
D)whether the distribution is skewed.

Answer 2

C

Question 3

Figure:
The scatter diagram in figure 3.1 suggests that ______ relationship likely exists between 30-year mortgage rates and new home sales.

A)a positive linear
B)a negative linear
C)a quadratic
D)no linear

Answer 3

B

Question 4

Suppose that a data set contains 275 observations ranging from a low of 6,000 to a high of 70,000.What is the appropriate number of classes to use when constructing a histogram for the data?

A)6
B)7
C)8
D)9

Question 5

An outlier is

A)a data point that falls more than two standard deviations away from the mean.
B)a data point that falls more than three standard deviations away from the mean.
C)a data point that exceeds the median.
D)a data point that falls below zero.

Question 6

Figure:
The scatter diagram in figure 3.2 suggests that _______ relationship likely exists between the price and quantity supplied of surfboards.

A)a positive linear
B)a negative linear
C)a quadratic
D)no linear

Question 7

A data set is said to be skewed to the left if

A)an outlier falls more than three standard deviations below the sample mean.
B)an outlier falls more than three standard deviations above the sample mean.
C)an outlier falls more than three standard deviations below the sample median.
D)an outlier falls more than three standard deviations above the sample median.

Question 8

A smaller standard deviation of a distribution indicates that

A)the observations in a data set are closer together.
B)the observations in a data set are farther apart.
C)a smaller mean.
D)the mean and median are closer together.

Question 9

The standard deviation of a distribution is the

A)total distance that data points fall away from the mean.
B)sum of the distances that data points fall away from the mean.
C)variance of the data points in the distribution.
D)average distance that data points fall away from the mean.

Question 10

When is the median most appropriate for summarizing a data set?

A)Always.
B)When the data set contains outliers.
C)When the data set is symmetric.
D)When the data are closely distributed to each other.

Question 11

The mean is the

A)middle number in an ordered data set.
B)most frequently observed value in a data set.
C)sum of the individual observation divided by the number of observations.
D)only relevant measure of central tendency.

Question 12

Figure:
The scatter diagram in figure 3.3 suggests that ______ relationship likely exists between daily rainfall and the Dow Jones industrial average.

A)a positive linear
B)a negative linear
C)a quadratic
D)no linear

Question 13

If a data set is skewed then

A)the mean is the most appropriate measure of central tendency.
B)the mean is the most appropriate measure of dispersion.
C)the median is the most appropriate measure of central tendency.
D)the median is the most appropriate measure of dispersion.

Question 14

An outlier that is much larger than the remaining values in a data set will cause the data set to be

A)skewed to the left.
B)skewed to the right.
C)symmetric.
D)unskewed.

Question 15

The median is the

A)middle number in an ordered data set.
B)most frequently observed value in a data set.
C)sum of the individual observation divided by the number of observations.
D)only relevant measure of central tendency.

Question 16

An outlier that is much smaller than the remaining values in a data set will cause the data set to be

A)skewed to the left.
B)skewed to the right.
C)symmetric.
D)unskewed.

Question 17

Relative frequency histograms are potentially valuable because they

A)provide a visual overview of the distribution of the data.
B)are often presented in media outlets.
C)show the mean,the median,and the mode of the sample.
D)are pretty to look at.

Question 18

Identifying outliers is

A)important because data sets with outliers are best summarized by the sample mean.
B)never important.
C)important because data sets with outliers are often skewed.
D)important because outliers decrease the sample variance.

Question 19

When is the mean most appropriate for summarizing a data set?

A)Always.
B)When the data set contains outliers.
C)When the data set is symmetric.
D)When the data are skewed to the right.

Question 20

A scatter diagram is potentially valuable because it

A)visually depicts the relationship between two variables.
B)visually depicts the median of the sample.
C)visually depicts the standard deviation of the sample.
D)visually depicts the distribution of a variable.

Question 21

The correlation coefficient is generally preferred to the covariance because

A)the correlation coefficient is a unit free measure of linear association.
B)the covariance is bounded to fall between -1 and 1.
C)the correlation coefficient must be positive.
D)the covariance measures the quadratic relationship between two random variables.

Question 22

a.If the correlation coefficient between two random variables equals zero,does that imply that there is no relationship between those random variables?
b.If the correlation coefficient between two random variables is close to one in absolute value,does that imply that one random variable causes another random variable?

Question 23

The correlation coefficient is

A)must be positive.
B)the square root of the covariance.
C)must be negative.
D)must fall between -1 and 1.

Question 24

Suppose you have collected the data in Table 3.1.
Calculate the mean,median,mode,variance,and standard deviation.Interpret these values.

Question 25

The covariance

A)measures the linear relationship between two random variables.
B)must fall between -1 and 1.
C)must be positive.
D)measures the quadratic relationship between two random variables.

Question 26

Suppose that you construct the histogram in Figure 3.4.
What conclusions would you draw about the data? Explain.

Question 27

In your own words,describe the potential benefits of constructing a histogram to summarize a given data set.

Question 28

List and describe the steps involved in constructing a histogram.

Question 29

A counselor working with teenagers is interested in the relationship between anxiety and depression.The counselor administers a depression and anxiety test to each teenager.The scores obtained from the administration of the two inventories are given below.

a.What do these data say about the level of anxiety and depression in these teenagers?
b.What is the correlation between anxiety and depression? What does this number tell you?
c.What is the correlation coefficient between anxiety and depression? What does this number tell you?
d.If you were counseling a teenager with high levels of anxiety,what would you expect their level of depression to be?