Question 1

Which of the following best describes the shape of the distribution of average wind speeds in Hopkins Memorial Forest, as shown in the histogram?

Accepted Answer

Skewed to the right (positively skewed)

Question 2

Given the 5-number summary for average wind speed (Min: 0.00, Q1: 0.46, Median: 1.12, Q3: 2.28, Max: 6.73), what is the interquartile range (IQR)?

$$	ext{IQR} = Q_3$ - Q_1$

Accepted Answer

$$1.82$$

Question 3

Which of the following is NOT a step in constructing a boxplot?

Accepted Answer

Draw whiskers to the minimum and maximum values, regardless of outliers

Question 4

If the lower fence for outliers is calculated as $$Q_1 - 1.5$$ 	imes 	ext{IQR}$$ and the upper fence as Q_3$ + 1.5 	imes 	ext{IQR}$$, what are the values of the fences for the wind speed data (Q1 = 0.46, Q3 = 2.28, IQR = 1.82)?

Accepted Answer

Lower: $$-2.27$$, Upper: $$5.01$$

Question 5

Why is it important to use the same horizontal scale when comparing histograms of two groups?

Accepted Answer

It allows for a fair visual comparison of the distributions

Question 6

Which summary statistic is most resistant to the effect of outliers?

Accepted Answer

Median

Question 7

Suppose you find an outlier in your data. What is the best initial action according to statistical best practices?

Accepted Answer

Investigate the cause of the outlier

Question 8

Given the following summary statistics for wind speed by season:

Summer: Mean = 1.11, StdDev = 1.10, Median = 0.71, IQR = 1.27
Winter: Mean = 1.90, StdDev = 1.29, Median = 1.72, IQR = 1.82

Which season is both windier and more variable?

Accepted Answer

Winter

Question 9

A boxplot is most useful for which of the following tasks?

Accepted Answer

Comparing the medians and spreads of several groups

Question 10

If a data set has a minimum value of 0, Q1 of 0.46, median of 1.12, Q3 of 2.28, and a maximum of 6.73, which value would be considered a 'far outlier' using the rule $$Q_3 + 3$$ 	imes 	ext{IQR}$$?

Accepted Answer

Any value greater than $$7.74$$

Question 11

Which of the following is a common cause of outliers in a data set?

Accepted Answer

A respondent misunderstanding the survey question

Question 12

When comparing more than two groups, which graphical display is generally preferred?

Accepted Answer

Boxplot

Question 13

A researcher finds that the range of Kentucky Derby winning times from 1875 to 2016 is much larger than the range from 1896 to 2016. What is the most likely explanation?

Accepted Answer

The distance of the race changed, affecting the times

Question 14

Which of the following statements about outliers is FALSE?

Accepted Answer

Outliers should always be removed from the data set

Question 15

If the median is much closer to Q1 than to Q3 in a boxplot, what does this suggest about the distribution?

Accepted Answer

The distribution is skewed to the right

Question 16

Which of the following is NOT included in the 5-number summary?

Accepted Answer

Mean

Question 17

A boxplot for monthly wind speeds shows several points plotted beyond the whiskers in April and December. What does this indicate?

Accepted Answer

There are outliers in April and December

Question 18

Which of the following best describes the main advantage of boxplots over histograms when comparing multiple groups?

Accepted Answer

Boxplots are more compact and allow for easy side-by-side comparison

Question 19

If you analyze your data both with and without outliers, what should you do when presenting your results?

Accepted Answer

Present both results and explain your reasoning

Understanding and Comparing Distributions in Introductory Statistics

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