AP Statistics Practice Quiz: Summary Statistics for 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 16 questions to check your progress.

Question 1 of 16

A researcher collects data on the heights of 50 randomly selected students from a university. She calculates the average height of these students. What is this average height an example of?

A)A parameterB)A statisticC)A populationD)A variable

All Questions (16)

A researcher collects data on the heights of 50 randomly selected students from a university. She calculates the average height of these students. What is this average height an example of?

A) A parameter

B) A statistic

C) A population

D) A variable

Correct Answer: B

According to the provided content, a statistic is a numerical summary of sample data. The average height is a numerical summary calculated from the sample of 50 students.

Consider the following dataset of test scores: {72, 85, 88, 90, 95}. What is the mean of this dataset?

A) 85

B) 86

C) 88

D) 90

Correct Answer: B

The mean is the sum of the data values divided by the number of values. The sum is 72 + 85 + 88 + 90 + 95 = 430. The number of values is 5. Therefore, the mean is 430 / 5 = 86.

For the ordered dataset {10, 15, 20, 25, 30, 35, 40}, which value represents the median?

A) 20

B) 22.5

C) 25

D) 30

Correct Answer: C

The median is the middle value of an ordered data set. In this set of 7 values, the middle value is the 4th one, which is 25.

A dataset of home prices is known to be right-skewed due to a few very expensive mansions. Which pair of measures is most appropriate for describing the center and variability of the home prices?

A) Mean and standard deviation

B) Mean and interquartile range (IQR)

C) Median and interquartile range (IQR)

D) Median and range

Correct Answer: C

For skewed data with outliers, resistant measures are preferred. The median and IQR are resistant to the influence of outliers, while the mean, standard deviation, and range are nonresistant. Therefore, median and IQR provide a more accurate description of a typical home price and its spread.

Given the five-number summary for a dataset: Minimum=10, Q1=25, Median=40, Q3=60, Maximum=100. What is the interquartile range (IQR)?

A) 15

B) 35

C) 50

D) 90

Correct Answer: B

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). Here, IQR = Q3 - Q1 = 60 - 25 = 35.

An extreme outlier is added to a dataset. Which of the following measures is likely to be LEAST affected?

A) Mean

B) Standard deviation

C) Range

D) Median

Correct Answer: D

The median and IQR are resistant to outliers. The mean, standard deviation, and range are nonresistant. The median, being the middle value, will not change significantly (or at all) with the addition of a single extreme value, making it the least affected among the choices.

If a student's exam score is at the 80th percentile, what does this mean?

A) The student scored 80% on the exam.

B) 80% of students scored higher than this student.

C) 80% of the data is less than or equal to the student's score.

D) The student's score is 80% of the highest score in the class.

Correct Answer: C

The Pth percentile is defined as the value that has p% of the data less than or equal to it. Therefore, the 80th percentile means 80% of the scores are less than or equal to this student's score.

For a particular dataset, the first quartile (Q1) is 50 and the third quartile (Q3) is 80. According to the 1.5xIQR rule, a value would be considered a high outlier if it is greater than what number?

A) 95

B) 110

C) 120

D) 125

Correct Answer: D

First, calculate the IQR: IQR = Q3 - Q1 = 80 - 50 = 30. An outlier is a value more than 1.5xIQR beyond the quartiles. The upper boundary for outliers is Q3 + 1.5(IQR). So, 80 + 1.5(30) = 80 + 45 = 125. Any value greater than 125 would be a high outlier.

The salaries of employees at a company are measured in dollars. If every employee receives a $2,000 end-of-year bonus, how would the standard deviation of the salaries change?

A) It would increase by $2,000.

B) It would increase by the square root of $2,000.

C) It would decrease by $2,000.

D) It would not change.

Correct Answer: D

Changing units of measurement affects calculated statistics. Specifically, adding a constant to every value in a dataset changes measures of center (like the mean and median) but does not change measures of variability (like range, IQR, and standard deviation). Since the spread of the data remains the same, the standard deviation does not change.

Which of the following statements correctly describes the relationship between variance and standard deviation?

A) The variance is the square root of the standard deviation.

B) The standard deviation is the square of the variance.

C) The variance is the square of the standard deviation.

D) The standard deviation is twice the variance.

Correct Answer: C

The provided content states that the standard deviation measures variability and its square is called the variance. Therefore, variance = (standard deviation)^2.

Consider the dataset {5, 10, 12, 15, 20, 100}. Which of the following statements is true?

A) The mean is less than the median.

B) The mean is greater than the median.

C) The mean is equal to the median.

D) The relationship cannot be determined without calculation.

Correct Answer: B

The value 100 is an outlier. The mean is nonresistant to outliers and will be pulled up by this large value. The median is resistant and will be the average of the two middle numbers (12 and 15), which is 13.5. The mean will be (5+10+12+15+20+100)/6 = 27. Thus, the mean is greater than the median, which is characteristic of a right-skewed distribution or a dataset with a high outlier.

The heights of a group of people have a mean of 68 inches and a standard deviation of 3 inches. According to one common rule, a height would be considered an outlier if it is outside of which range?

A) 65 to 71 inches

B) 62 to 74 inches

C) 59 to 77 inches

D) 67 to 69 inches

Correct Answer: B

Outliers can be identified as values that are 2 or more standard deviations from the mean. The range within 2 standard deviations is Mean ± 2(SD). This is 68 ± 2(3), which is 68 ± 6. The range is from 62 to 74 inches. Any value outside this range would be considered an outlier.

For the dataset {2, 5, 8, 10, 15, 20}, what are the first quartile (Q1) and third quartile (Q3)?

A) Q1 = 5, Q3 = 15

B) Q1 = 6.5, Q3 = 17.5

C) Q1 = 5, Q3 = 17.5

D) Q1 = 8, Q3 = 10

Correct Answer: A

The data is already ordered. The median is the average of the two middle values (8 and 10), which is 9. The lower half of the data is {2, 5, 8}. The median of this lower half is Q1, which is 5. The upper half of the data is {10, 15, 20}. The median of this upper half is Q3, which is 15.

Which of the following is NOT a measure of variability?

A) Range

B) Standard Deviation

C) Interquartile Range (IQR)

D) Median

Correct Answer: D

Range, interquartile range (IQR), and standard deviation are all common measures of variability. The median is a measure of center or position, not variability.

The lengths of fish in a lake are measured in centimeters. A biologist decides to convert all measurements to millimeters by multiplying by 10. How will this conversion affect the range and the mean of the data?

A) Both the range and the mean will be multiplied by 10.

B) The range will be multiplied by 100, and the mean will be multiplied by 10.

C) The range will be multiplied by 10, but the mean will not change.

D) Neither the range nor the mean will change.

Correct Answer: A

Changing units of measurement affects calculated statistics. When all data values are multiplied by a constant (in this case, 10), all measures of center (like the mean) and measures of variability (like the range) are also multiplied by that same constant.

Which of the following pairs of statistics are considered resistant to outliers?

A) Mean and standard deviation

B) Median and range

C) Mean and range

D) Median and interquartile range (IQR)

Correct Answer: D

The content explicitly states that the mean, standard deviation, and range are nonresistant to outliers, while the median and IQR are resistant. Therefore, the pair of resistant statistics is the median and IQR.