Free Practice Quiz Question List

3. Numerical Summaries and Comparing Distributions Online Quiz Questions

Use this free practice quiz with 20 questions to review 3. Numerical Summaries and Comparing Distributions, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Which statement best explains why the median is often preferred to the mean for a distribution containing an influential outlier?

A
The mean is always less than the median.
B
The median is generally more resistant to extreme observations than the mean.
C
The mean ignores the sizes of the observations.
D
The median must equal the mean in a skewed distribution.

Choose all

1 point

Select all statements that correctly describe the interquartile range (IQR).

A
The interquartile range is resistant to outliers.
B
The standard deviation is completely unaffected by outliers.
C
The interquartile range describes the spread of the middle 50% of observations.
D
The range is resistant because it uses all observations.

True or false

1 point

In a right-skewed distribution, the mean is typically greater than the median.

A
True
B
False

Written response

1 point

For the data values 4, 5, 6, 7, and 28, what is the range?

Fill in the blank

1 point

The measures the typical distance of observations from the mean.

Choose one

1 point

Which list gives the five-number summary in the correct order?

A
Mean, median, mode, range, standard deviation
B
Minimum, mean, median, IQR, maximum
C
Minimum, first quartile, median, third quartile, maximum
D
Minimum, first percentile, median, ninety-ninth percentile, maximum

Choose all

1 point

Select all measures that are generally sensitive to outliers.

A
The median is usually highly sensitive to one extreme observation.
B
The mean can be pulled toward an outlier.
C
The IQR must increase dramatically whenever one outlier is added.
D
The standard deviation can increase substantially because of an outlier.

Written response

1 point

An exam score is 91, the mean is 75, and the standard deviation is 8. What is the z-score?

Fill in the blank

1 point

In the 1.5-IQR rule, the boundary calculated as Q3 plus 1.5 times the IQR is called the .

True or false

1 point

If a test score distribution has mean 78 and standard deviation 6, then every score must lie between 72 and 84.

A
True
B
False

Open ended

1 point

A household travel-time distribution is right-skewed and has one unusually long trip. Its median is 31 minutes and its IQR is 18 minutes. Write a concise statistical description that chooses appropriate summaries and interprets both reported values.

Choose one

1 point

Commute times are measured in minutes. In what units should their standard deviation be reported?

A
Minutes squared
B
Minutes
C
No units
D
Percentiles

Choose one

1 point

A quantitative distribution is strongly right-skewed because of one unusually large observation. Which measure of center is generally the most appropriate for describing a typical observation?

A
The mean, because it uses every observation
B
The median, because it is resistant to extreme observations
C
The range, because it uses the middle half of the data
D
The standard deviation, because it identifies the middle observation

Choose one

1 point

Which measure describes the spread of the middle 50% of a quantitative distribution?

A
The range
B
The standard deviation
C
The interquartile range
D
The mean

Choose one

1 point

An exam score has a positive z-score. What does this indicate about the score relative to the reference distribution's mean?

A
The score is above the mean
B
The score is below the mean
C
The score is exactly at the mean
D
The score must be an outlier

Choose one

1 point

Using the 1.5-IQR rule, which expression gives the upper fence used to flag possible high outliers?

A
The minimum minus 1.5 times the range
B
The first quartile minus 1.5 times the IQR
C
The third quartile minus 1.5 times the IQR
D
The third quartile plus 1.5 times the IQR

Choose one

1 point

Commute times are measured in minutes. In what units is their standard deviation expressed?

A
It is measured in squared minutes
B
It is measured in minutes
C
It is measured as a unit-free percentile
D
It is measured in percentage points

True or false

1 point

True or false: The empirical rule should be applied automatically to any quantitative distribution, regardless of its shape.

A
True
B
False

Written response

1 point

An exam has mean score 75 and standard deviation 8. A student scores 91. What is the student's z-score? Enter the answer as a number.

Written response

1 point

A distribution of household travel times is right-skewed and contains one unusually long trip. Which single measure of center is generally most appropriate to report?