Checkpoint Quiz: Quantifying Variability Relative to the Median

Here is the 5-number summary for a group of 100 runners in a 5-kilometer race. The variable is the time to complete the race:

Five-number summary:

Minimum: 15 minutes

Q1: 27 minutes

Median: 31 minutes

Q3: 32 minutes

Maximum: 50 minutes

Which one of the following statements about the distribution is most accurate?

At least 25 runners had times ranging from 31 minutes to 32 minutes.

Below is the five-number summary for 136 hikers who recently completed the John Muir Trail (JMT). The variable is the amount of time to complete the 212-mile hike from Yosemite Valley across the high Sierras to the top of Mount Whitney.

Five-number summary:

Minimum: 9 days

Q1: 18 days

Median: 21 days

Q3: 28 days

Maximum: 56 days

Which one of the following statements about the distribution is most accurate?

At least 34 hikers completed the JMT within 28 to 56 days.

The boxplots below give the cardiovascular disease (CVD) rate as a percentage of total deaths for 155 countries.

Which of the following statements is a valid conclusion that can be drawn from the boxplots? Check all that apply.

-The medians are close. This suggests that the typical CVD mortality rate is about the same for both groups of countries.

-If we use range as a measure of variability, then the group of countries with a low per-capita supply of vegetable protein has more variability.

-If we use the interquartile range as a measure of variability, then the group of countries with a low per-capita supply of vegetable protein has less variability.

In a survey, students at two community colleges estimated the hours they spend on Facebook each week.

Which of the following statements is a valid conclusion that can be drawn from the boxplots? Check all that apply.

-The medians are close; they differ by about half an hour. This suggests that the typical student at each college spends about the same amount of time on Facebook each week.

-If we use range as a measure of variability, then College B has more variability.

-If we use the interquartile range as a measure of variability, then College B has less variability.

Here are three boxplots on an unlabeled number line.

Which boxplot has the following five-number summary?

Min = 1

Q1 = 5

Q2 = 6.5

Q3 = 9

Max = 11

Boxplot C:

Five-number summary information:

The first quartile between the minimum and Q1 has more variability (5 - 1 = 4) than the fourth quartile between Q3 and the maximum (11 - 9 = 2).

The second quartile between Q1 and Q2 has less variability (6.5 - 5 = 1.5) than the third quartile between Q2 and Q3 (9 - 6.5 = 2.5).

Boxplot C information:

The first quartile between the minimum and Q1 has more variability (spread) than the fourth quartile between Q3 and the maximum.

The second quartile between Q1 and Q2 has less variability (spread) than the third quartile between Q2 and Q3.

Therefore, the five-number summary fits Boxplot C.

Here are three boxplots on an unlabeled number line.

Which boxplot has the following five-number summary?

Min = 0

Q1 = 0.5

Q2 = 2

Q3 = 3

Max = 6

Boxplot B:

Information from the five-number summary:

The first quartile between the minimum and Q1 has the least amount of variability (0.5 - 0 = 0.5).

The second quartile between Q1 and Q2 has slightly more variability (2 - 0.5 = 1.5) than third quartile between Q2 and Q3 (3 - 2 = 1).

The fourth quartile between Q3 and the maximum has the most amount of variability (6 - 3 = 3).

Boxplot B observations:

The first quartile between the minimum and Q1 has the least amount of variability.

The second quartile between Q1 and Q2 has slightly more variability than the third quartile between Q2 and Q3.

The fourth quartile between Q3 and the maximum has the most amount of variability.

So the five-number summary fits Boxplot B.

Here is the five-number summary for a group of 100 runners in a 5-kilometer race. The variable is the time to complete the race.

Five-number summary:

Minimum: 15 minutes

Q1: 27 minutes

Median: 31 minutes

Q3: 32 minutes

Maximum: 50 minutes

Are there any outliers in the runners' finish times by the 1.5 * IQR definition?

Both the slowest and the fastest runners are outliers.

Below is the five-number summary for 136 hikers who recently completed the John Muir Trail (JMT). The variable is the amount of time to complete the 212-mile hike from Yosemite Valley across the high Sierras to the top of Mount Whitney.

Five-number summary:

Minimum: 9 days

Q1: 18 days

Median: 21 days

Q3: 28 days

Maximum: 56 days

If we use the 1.5 * IQR rule to determine whether there are any outliers, what is the left boundary?

3

Below is the five-number summary for 136 hikers who recently completed the John Muir Trail (JMT). The variable is the amount of time to complete the 212-mile hike from Yosemite Valley across the high Sierras to the top of Mount Whitney.

Five-number summary:

Minimum: 9 days

Q1: 18 days

Median: 21 days

Q3: 28 days

Maximum: 56 days

If we use the 1.5 * IQR rule to determine whether there are any outliers, what is the right boundary?

43