AP Statistics Practice Quiz: Graphical Representations of Summary Statistics

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

Which of the following collections of values constitutes the five-number summary for a set of quantitative data?

A)Mean, Median, Mode, Range, Standard DeviationB)Minimum, First Quartile (Q1), Median, Third Quartile (Q3), MaximumC)Minimum, Mean, Median, Mode, MaximumD)First Quartile (Q1), Second Quartile (Q2), Third Quartile (Q3), Fourth Quartile (Q4), Fifth Quartile (Q5)

All Questions (15)

Which of the following collections of values constitutes the five-number summary for a set of quantitative data?

A) Mean, Median, Mode, Range, Standard Deviation

B) Minimum, First Quartile (Q1), Median, Third Quartile (Q3), Maximum

C) Minimum, Mean, Median, Mode, Maximum

D) First Quartile (Q1), Second Quartile (Q2), Third Quartile (Q3), Fourth Quartile (Q4), Fifth Quartile (Q5)

Correct Answer: B

Based on the provided content, the five-number summary is explicitly defined as consisting of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

A boxplot is a graphical tool specifically designed to represent which set of summary statistics?

A) The mean and standard deviation

B) The frequency and relative frequency of categories

C) The five-number summary

D) The shape, center, and spread using a histogram

Correct Answer: C

The provided content explicitly states that 'A boxplot is a graphical representation of the five-number summary.'

In a standard boxplot, the value that divides the data into the lower 50% and the upper 50% is represented by what feature?

A) The end of the left whisker

B) The line inside the box

C) The right edge of the box

D) The end of the right whisker

Correct Answer: B

The line inside the box of a boxplot represents the median. The median is a component of the five-number summary and is the value that separates the lower 50% from the upper 50% of the data.

For a distribution of quantitative data that is strongly skewed to the right, what is the most likely relationship between the mean and the median?

A) The mean will be approximately equal to the median.

B) The mean will be less than the median.

C) The mean will be greater than the median.

D) The relationship cannot be determined from the skewness.

Correct Answer: C

The content states that the relationship between the mean and median is affected by skewness. In a right-skewed distribution, high-value outliers pull the mean towards the tail (the right side), making it greater than the median.

A real estate agent creates a boxplot of home prices in a neighborhood. The boxplot shows that the third quartile (Q3) is $500,000. Which of the following claims can be justified using this summary statistic?

A) The most expensive house in the neighborhood costs $500,000.

B) Approximately 75% of the homes in the neighborhood are priced at or below $500,000.

C) The average home price in the neighborhood is $500,000.

D) Exactly 25% of the homes are priced at exactly $500,000.

Correct Answer: B

The third quartile (Q3) is a value in the five-number summary that marks the 75th percentile. This means that 75% of the data falls at or below this value. Therefore, this summary statistic can be used to justify the claim.

Which component of the five-number summary represents the 25th percentile of a quantitative dataset?

A) The minimum

B) The first quartile (Q1)

C) The median

D) The third quartile (Q3)

Correct Answer: B

The first quartile (Q1) is defined as the 25th percentile, meaning that 25% of the data values are less than or equal to Q1. It is a key component of the five-number summary.

A boxplot of student test scores shows a long right whisker and the median line is shifted to the left side of the box. Based on this graphical representation, what can be inferred about the relationship between the mean and median score?

A) The mean score is likely lower than the median score.

B) The mean score is likely higher than the median score.

C) The mean score is likely identical to the median score.

D) The boxplot does not provide information about the mean.

Correct Answer: B

The features described (long right whisker, median shifted left in the box) indicate a right-skewed distribution. The content states that skewness affects the relationship between mean and median. In a right-skewed distribution, the mean is pulled higher than the median by the high-value scores.

A boxplot is created for the daily commute times for a group of employees. The box portion of the plot spans from 20 minutes to 45 minutes. What does this represent?

A) The full range of commute times is 25 minutes.

B) The average commute time is between 20 and 45 minutes.

C) The middle 50% of commute times fall between 20 and 45 minutes.

D) 50% of employees have a commute time of exactly 20 minutes or 45 minutes.

Correct Answer: C

A boxplot graphically represents the five-number summary. The box itself represents the range between the first quartile (Q1) and the third quartile (Q3), which contains the middle 50% of the data.

What is the primary purpose of using a graphical representation like a boxplot for summary statistics?

A) To list every individual data point in the dataset.

B) To provide a visual summary of the center and spread of the data.

C) To calculate the exact mean and standard deviation.

D) To prove a hypothesis with absolute certainty.

Correct Answer: B

The provided content states that we can 'represent summary statistics for quantitative data graphically' and 'describe summary statistics...represented graphically.' A boxplot achieves this by visually summarizing the five-number summary, which provides key information about the center (median) and spread (range, IQR) of the data.

The five-number summary for the salaries (in thousands of dollars) at a small company is: Minimum=30, Q1=45, Median=55, Q3=70, Maximum=150. Which of the following claims is best justified by these statistics?

A) The distribution of salaries is symmetric.

B) The mean salary is likely lower than the median salary.

C) More than half of the employees earn a salary above $60,000.

D) The distribution of salaries is skewed to the right.

Correct Answer: D

The distance from the median (55) to the maximum (150) is 95, while the distance from the minimum (30) to the median is 25. This large difference indicates a long tail on the right side of the distribution, which is characteristic of a right-skewed distribution. This skewness would pull the mean higher than the median.

For a distribution of quantitative data that is approximately symmetric, what is the most likely relationship between the mean and the median?

A) The mean will be significantly greater than the median.

B) The mean will be significantly less than the median.

C) The mean and the median will be approximately equal.

D) The median will be exactly half of the mean.

Correct Answer: C

The content states that skewness affects the relationship between the mean and median. In an approximately symmetric distribution, there is little to no skew. Therefore, the mean and median will be located at approximately the same point, as there are no extreme values pulling the mean in one direction.

A boxplot representing the heights of a sample of adult males has its left whisker extending to 62 inches. What does this value represent?

A) The first quartile (Q1) of the heights.

B) The median height.

C) The minimum height in the sample.

D) The mean height.

Correct Answer: C

A boxplot is a graphical representation of the five-number summary. The end of the left whisker represents the minimum value in the dataset (assuming no outliers are plotted separately).

A boxplot for the ages of attendees at a concert shows the following five-number summary: 16, 19, 22, 28, 45. Which statement accurately describes the distribution of ages?

A) 50% of the attendees are between 16 and 22 years old.

B) The range of ages for the middle 50% of attendees is 9 years.

C) The distribution of ages is perfectly symmetric.

D) The mean age of the attendees is 22 years old.

Correct Answer: B

The box of the boxplot represents the middle 50% of the data, spanning from Q1 (19) to Q3 (28). The range of this box, the interquartile range, is Q3 - Q1 = 28 - 19 = 9 years. This is the most accurate description that can be derived from the provided summary statistics.

A researcher presents a boxplot of daily rainfall amounts. The boxplot shows the median is 0.5 inches. Based solely on this graphical representation of the five-number summary, which claim is NOT justified?

A) On half of the days observed, the rainfall was 0.5 inches or less.

B) The most frequent rainfall amount (the mode) was 0.5 inches.

C) The center of the rainfall distribution, as measured by the median, is 0.5 inches.

D) The 50th percentile of daily rainfall is 0.5 inches.

Correct Answer: B

A boxplot represents the five-number summary and does not provide information about the frequency of individual data values. Therefore, the mode (the most frequent value) cannot be determined from a boxplot. The other options are all valid interpretations of the median.

If a graphical representation of a dataset shows a distribution that is skewed to the left, which of the following is the most likely consequence for its summary statistics?

A) The mean will be pulled to the left of the median.

B) The mean will be pulled to the right of the median.

C) The first quartile (Q1) will be greater than the third quartile (Q3).

D) The minimum value will be equal to the median.

Correct Answer: A

The provided content states that the relationship between the mean and median is affected by skewness. In a left-skewed distribution, low-value outliers or a long tail to the left will pull the mean towards these lower values, resulting in the mean being less than (to the left of) the median.