Question 1

Which of the following best describes the distribution of average wind speeds in Hopkins Memorial Forest during 2011?

Accepted Answer

Unimodal and skewed right

Question 2

Given the following five-number summary for wind speeds: Min = 0.00, Q1 = 0.46, Median = 1.12, Q3 = 2.28, Max = 6.73, what is the interquartile range (IQR)?

Accepted Answer

$$\mathrm{IQR} = 2.28 - 0.46 = 1.82$$

Question 3

When comparing the wind speeds in summer and winter, which season shows greater variability and how is this reflected in the summary statistics?

Accepted Answer

Winter, as shown by a higher standard deviation and IQR

Question 4

Which graphical display is most effective for comparing the distributions of several groups and identifying outliers?

Accepted Answer

Boxplot

Question 5

A boxplot has a median that is not centered in the box and a longer upper whisker. What does this indicate about the distribution?

Accepted Answer

The distribution is skewed right

Question 6

In a back-to-back stem-and-leaf plot comparing nest egg indices for Northeast/Midwest and South/West regions, what does it mean if most values for Northeast/Midwest are above 100 and higher than any in South/West?

Accepted Answer

Northeast/Midwest states have higher nest egg indices than South/West

Question 7

Suppose you are comparing four types of coffee cups for heat retention. The Nissan cup has the smallest IQR and typically loses only 2°F after 30 minutes. What does this suggest about the Nissan cup's performance?

Accepted Answer

It is a consistent performer and retains heat best

Question 8

A researcher shuffles the direction labels (up/down street) for car speeds and calculates the difference in means 10,000 times. What statistical concept is being illustrated?

Accepted Answer

Permutation test (randomization test)

Question 9

If a CEO's reported height is 170 inches, which is an outlier, what is the most likely cause according to common errors?

Accepted Answer

There was confusion about units (measured in centimeters)

Question 10

Which transformation is commonly used to make a right-skewed distribution more symmetric?

Accepted Answer

Take the logarithm ($$\log x)$$

Question 11

After applying a log transformation to CEO compensation data, the distribution becomes more symmetric. What is a key benefit of this transformation?

Accepted Answer

It makes measures of center and spread more meaningful

Question 12

Which of the following is NOT a recommended step when encountering an outlier in your data?

Accepted Answer

Ignore the outlier without investigation

Question 13

A boxplot comparing steel and wooden roller coasters shows steel coasters have a much wider range and a superfast outlier. What does this suggest about steel coasters?

Accepted Answer

Steel coasters have greater variability and include exceptionally fast rides

Question 14

If a distribution is left-skewed, which transformation might help make it more symmetric?

Accepted Answer

Square the data ($$x^2)$$

Question 15

Why are boxplots particularly useful when comparing multiple groups?

Accepted Answer

They provide a clear summary of center, spread, and outliers for each group

Question 16

Which of the following is a guideline for identifying outliers using the IQR?

Accepted Answer

Any value greater than $$Q_3 + 1.5$$ 	imes \mathrm{IQR}$$ or less than Q_1$ - 1.5 	imes \mathrm{IQR}$$

Question 17

A histogram of wind speeds in summer months is unimodal and skewed right. What does this imply about most summer days?

Accepted Answer

Most summer days have low wind speeds, with a few very windy days

Question 18

When comparing boxplots side by side, what does it mean if one group has a higher median and a larger IQR than another?

Accepted Answer

The group has a higher center and greater variability

Question 19

If a data set contains an extraordinary value, such as a roller coaster with a speed much higher than all others, what should you do?

Accepted Answer

Investigate the cause and comment on the outlier

Question 20

Which of the following is a potential pitfall when re-expressing data using logarithms?

Accepted Answer

Applying the log transformation to negative or zero values

Understanding and Comparing Distributions: Visual Displays, Summaries, and Transformations

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