AP Statistics Practice Quiz: Describing the Distribution of a Quantitative Variable

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 15 questions to check your progress.

Question 1 of 15

According to the provided text, which of the following are the primary characteristics used to describe a quantitative data distribution?

A)Mean, median, mode, and rangeB)Shape, center, variability, and unusual featuresC)Skew, peaks, gaps, and clustersD)Symmetry, modality, population, and sample

All Questions (15)

According to the provided text, which of the following are the primary characteristics used to describe a quantitative data distribution?

A) Mean, median, mode, and range

B) Shape, center, variability, and unusual features

C) Skew, peaks, gaps, and clusters

D) Symmetry, modality, population, and sample

Correct Answer: B

The content explicitly states, 'Descriptions of quantitative data include shape, center, variability, and unusual features like outliers, gaps, clusters, or multiple peaks.'

A single data point that is unusually small or large relative to the rest of the data is defined as which of the following?

A) A cluster

B) A peak

C) An outlier

D) A gap

Correct Answer: C

The text defines outliers directly: 'Outliers are data points that are unusually small or large relative to the rest of the data.'

How is the skew of a distribution determined?

A) By the number of peaks in the distribution

B) By the location of the center of the data

C) By the presence of outliers

D) By the length of its tails

Correct Answer: D

The provided content specifies that 'A distribution's skew is determined by the length of its tails.'

A data distribution that has two distinct peaks would be best described as which of the following?

A) Unimodal

B) Bimodal

C) Symmetric

D) Uniform

Correct Answer: B

The text states that distributions can be described by their number of peaks, providing 'unimodal' and 'bimodal' as examples. Bimodal refers to a distribution with two peaks.

What is the primary limitation of descriptive statistics as outlined in the provided text?

A) They can only be used for symmetric distributions.

B) They are not useful for identifying the shape of a data set.

C) They summarize a data set but do not attribute its properties to a larger population.

D) They are less accurate than graphical representations of data.

Correct Answer: C

The text clearly states, 'Descriptive statistics summarize a data set but do not attribute its properties to a larger population.'

A distribution where the two halves are mirror images of each other is described as:

A) Skewed

B) Unimodal

C) Uniform

D) Symmetric

Correct Answer: D

The content defines symmetric distributions as having 'mirrored halves.'

In a histogram of student test scores, a researcher notices that there are no scores between 50 and 60, while there are many scores both below 50 and above 60. This region with no observed data is known as a:

A) Peak

B) Cluster

C) Gap

D) Outlier

Correct Answer: C

The text defines a gap as 'a region in a distribution with no observed data,' which matches the scenario described.

Concentrations of data, which are often separated by gaps, are referred to as:

A) Peaks

B) Clusters

C) Outliers

D) Tails

Correct Answer: B

The definition provided in the text is: 'Clusters are concentrations of data, usually separated by gaps.'

Which of the following is NOT considered an 'unusual feature' according to the provided list?

A) Outliers

B) Gaps

C) Variability

D) Clusters

Correct Answer: C

The text lists 'outliers, gaps, clusters, or multiple peaks' as unusual features. Variability is listed as one of the four main characteristics of a distribution (shape, center, variability, unusual features), not as an unusual feature itself.

A distribution that is described as approximately uniform has what characteristic?

A) It has one distinct peak.

B) It has a long tail to one side.

C) The data values are spread out evenly.

D) It has several large gaps.

Correct Answer: C

The text states that distributions can be described as 'approximately uniform.' While not explicitly defined, a uniform distribution implies that data is spread evenly, contrasting with distributions that have peaks or clusters.

A statistician is analyzing a dataset of commute times. They note two distinct groupings of times: one around 15 minutes and another around 45 minutes, with very few commute times in between. How would this distribution be best described?

A) Symmetric and unimodal

B) Uniform with an outlier

C) Bimodal with a gap

D) Skewed with a cluster

Correct Answer: C

The two distinct groupings represent two peaks (bimodal) and the area with very few times in between represents a gap. This combines the concepts of peaks, clusters, and gaps.

An analyst calculates the mean and standard deviation for a sample of 100 customer satisfaction scores. Based on the provided text, what is the most appropriate conclusion?

A) These statistics describe the satisfaction of all customers of the company.

B) These statistics summarize the properties of the 100 scores in the sample.

C) These statistics prove that the distribution of scores is symmetric.

D) These statistics can be used to identify all outliers in the population.

Correct Answer: B

The text specifies that 'Descriptive statistics summarize a data set but do not attribute its properties to a larger population.' Therefore, the calculated mean and standard deviation only summarize the sample of 100 scores.

The term 'unimodal' is used to describe which characteristic of a quantitative data distribution?

A) Center

B) Variability

C) Shape

D) Unusual Features

Correct Answer: C

The text lists the number of peaks (unimodal, bimodal) as a way to describe the shape of a distribution.

Which statement best explains the relationship between clusters and gaps in a data distribution?

A) Clusters are regions with no data, while gaps are concentrations of data.

B) A distribution must have a cluster for every gap.

C) Clusters are concentrations of data that are often separated by gaps.

D) Gaps and clusters are both types of outliers.

Correct Answer: C

The text explicitly links the two concepts: 'Clusters are concentrations of data, usually separated by gaps.'

When describing a distribution, which of the following pairs of terms both relate to the shape of the distribution?

A) Center and variability

B) Outlier and gap

C) Skew and number of peaks

D) Cluster and center

Correct Answer: C

The provided text identifies skew (determined by tails) and the number of peaks (unimodal, bimodal) as descriptors of a distribution's shape. Outliers, gaps, and clusters are unusual features, while center and variability are separate primary characteristics.