Q: How are outliers identified in a boxplot?

Any value more than $$1.5 \times \text{IQR}$$ above Q3 or below Q1

Question 1

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

Accepted Answer

Skewed to the right and unimodal

Question 2

Given the five-number summary for average wind speed in Hopkins Forest (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 season is windier in Hopkins Forest based on the provided summary statistics and histograms?

Accepted Answer

Fall/Winter

Question 4

If you want to compare the number of cigarettes produced by two machines over 30 days, which graphical display is most effective for showing differences between the machines?

Accepted Answer

Side-by-side boxplots on the same horizontal scale

Question 5

A boxplot is constructed using which of the following components?

Accepted Answer

Five-number summary: minimum, Q1, median, Q3, maximum

Question 6

How are outliers identified in a boxplot?

Accepted Answer

Any value more than $$1.5 	imes 	ext{IQR}$$ above Q3 or below Q1

Question 7

Suppose the lower fence for a boxplot is calculated as $$Q_1 - 1.5$$ 	imes 	ext{IQR}$$. If Q_1$ = 0.46$$ and $$	ext{IQR} = 1.82$$, what is the value of the lower fence?

Accepted Answer

$$-2.27$$

Question 8

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

Accepted Answer

To make the differences between groups visually accurate and meaningful

Question 9

Which of the following is NOT a recommended way to handle outliers in a data set?

Accepted Answer

Remove outliers without explanation

Question 10

Given the summary statistics for wind speed by season, which season shows greater variability in wind speed, and how can you tell?

Accepted Answer

Winter, because it has a higher standard deviation and IQR

Question 11

If a data set has a median much less than the mean, what is the likely shape of its distribution?

Accepted Answer

Skewed to the right

Question 12

Which of the following statements about boxplots is TRUE?

Accepted Answer

Boxplots are ideal for comparing multiple groups side by side

Question 13

A researcher finds an outlier in the Kentucky Derby winning times. What should be her first step?

Accepted Answer

Investigate the cause of the outlier

Question 14

If the maximum wind speed in a data set is 6.73 mph and the minimum is 0.00 mph, what is the range?

Accepted Answer

$$6.73$$

Question 15

Which of the following is a limitation of histograms when comparing more than two groups?

Accepted Answer

Histograms become difficult to compare visually when there are more than two groups

Question 16

Suppose you have the following five-number summary for a data set: Min = 0, Q1 = 2, Median = 5, Q3 = 8, Max = 10. What is the value of the upper fence for identifying outliers?

$$	ext{Upper fence} = Q_3$ + 1.5 	imes (Q_3$ - Q_1$)$$

Accepted Answer

$$8 + 1.5 	imes 6 = 17$$

Question 17

Which of the following is NOT part of the five-number summary?

Accepted Answer

Mean

Question 18

If a boxplot shows several points plotted beyond the whiskers, what does this indicate?

Accepted Answer

There are outliers in the data

Question 19

Why might a researcher choose to present both the analysis with and without outliers?

Accepted Answer

To transparently show how outliers affect the results

Understanding and Comparing Distributions: Study Notes for Introductory Statistics

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