Q: Given the following data set: 4, 6, 6, 10, 10, 12, 22, 41, 122, calculate the interquartile range (IQR).

$$\text{IQR} = Q_3$ - Q_1$ = 31.5 - 6 = 25.5$$

Q: Which formula should you use to determine if a value is an outlier on the high end of a data set?

$$\text{Right Fence} = Q_3$ + 1.5 \times \text{IQR}$$

Q: A data set has the following five-number summary: Min = 2, Q1 = 5, Median = 8, Q3 = 12, Max = 20. Calculate the left fence for outliers.

$$\text{Left Fence} = Q_1$ - 1.5 \times (Q_3$ - Q_1$) = 5 - 1.5 \times (12 - 5) = 5 - 10.5 = -5.5$$

Question 1

Which of the following best describes the main advantage of a dot plot compared to a histogram or box plot when graphing quantitative data?

Accepted Answer

It retains individual data values, allowing for identification of exact observations.

Question 2

A histogram of earthquake magnitudes is shown to be symmetric and unimodal. Which measure of center and spread should you use to describe this data?

Accepted Answer

Mean and standard deviation

Question 3

Given the following data set: 4, 6, 6, 10, 10, 12, 22, 41, 122, calculate the interquartile range (IQR).

Accepted Answer

$$	ext{IQR} = Q_3$ - Q_1$ = 31.5 - 6 = 25.5$$

Question 4

Which of the following best describes a histogram that is approximately flat across all bins?

Accepted Answer

Uniform

Question 5

A box plot of earthquake magnitudes shows several points above the upper whisker. What does this indicate?

Accepted Answer

There are outliers on the high end of the data.

Question 6

If a data set is right-skewed, which measure of center is most appropriate to report?

Accepted Answer

Median

Question 7

Which formula should you use to determine if a value is an outlier on the high end of a data set?

Accepted Answer

$$	ext{Right Fence} = Q_3$ + 1.5 	imes 	ext{IQR}$$

Question 8

A histogram of the number of pets owned by students is right-skewed. Which of the following is most likely true?

Accepted Answer

Most students own a small number of pets, with a few owning many.

Question 9

Which of the following is NOT a feature that can be identified from a box plot?

Accepted Answer

The number of modes

Question 10

A data set has the following five-number summary: Min = 2, Q1 = 5, Median = 8, Q3 = 12, Max = 20. Calculate the left fence for outliers.

Accepted Answer

$$	ext{Left Fence} = Q_1$ - 1.5 	imes (Q_3$ - Q_1$) = 5 - 1.5 	imes (12 - 5) = 5 - 10.5 = -5.5$$

Question 11

Which of the following best describes a bimodal distribution?

Accepted Answer

A distribution with two distinct peaks or humps.

Question 12

A box plot is created for the number of penalty minutes for hockey players. One player has 122 minutes, while the rest are below 50. What does the box plot likely show?

Accepted Answer

A right-skewed distribution with an outlier at 122.

Question 13

Which of the following is a correct step when entering quantitative data into a calculator for statistical analysis?

Accepted Answer

Enter data values into L1 and leave FreqList blank for raw data.

Question 14

Which of the following is true about the effect of outliers on the mean and median?

Accepted Answer

Outliers pull the mean in their direction, but the median is less affected.

Question 15

A histogram of the average of three dice rolls is shown to be symmetric and bell-shaped. What is the most likely shape of the underlying distribution?

Accepted Answer

Normal (approximately symmetric and unimodal)

Question 16

Which of the following is NOT a required element when creating a histogram?

Accepted Answer

Show individual data values

Question 17

A city planner is analyzing the distribution of people per housing unit in several cities. The histogram is left-skewed. Which of the following is most likely true?

Accepted Answer

Most cities have a low number of people per housing unit, with a few cities having much lower values.

Question 18

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The difference between the first and third quartiles: $$	ext{IQR} = Q_3$ - Q_1$

Question 19

Which of the following is a correct interpretation of a unimodal distribution?

Accepted Answer

The distribution has one peak.

Graphing Quantitative Data: Shape, Center, and Spread

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