GRE Statistics: Mean, Median, Standard Deviation and 5 Practice Questions

Sriram Venkataraman

03/11/2026

7 min read

Statistics on the GRE is part of data analysis, one of the four content areas of Quantitative Reasoning. It covers descriptive statistics such as mean, median, mode, range, standard deviation, quartiles and percentiles, reading data from tables and graphs, and the normal distribution. Inferential statistics is not tested. Most GRE statistics questions reward knowing what each measure means rather than calculating it the long way.

This guide lists what ETS says the data analysis content covers, the definitions and shortcuts to know, how Data Interpretation sets work, and five practice questions with full solutions.

The five practice questions are written by Galvanize in the official GRE formats. They are not ETS questions. For the whole Quant section, read our GRE Quant guide; the other quant topic guides cover GRE algebra and GRE geometry.

What statistics is tested on the GRE?

ETS lists the data analysis topics on its Quantitative Reasoning content page:

• basic descriptive statistics, such as mean, median, mode, range, standard deviation, interquartile range, quartiles and percentiles
• interpretation of data in tables and graphs, such as line graphs, bar graphs, circle graphs, boxplots, scatterplots and frequency distributions
• elementary probability, including compound and independent events, and conditional probability
• random variables and probability distributions, including normal distributions
• counting methods, such as combinations, permutations and Venn diagrams

ETS says these topics are typically taught in high school algebra or introductory statistics courses, and that inferential statistics is not tested. This guide covers the statistics and data topics. Probability and counting have their own page: GRE probability questions with solutions.

How is the GRE Quant section set up?

The ETS test structure page sets out two Quant sections: 12 questions in 21 minutes, then 15 questions in 26 minutes, for 27 questions in 47 minutes. You get an on-screen calculator. ETS does not publish how many questions come from data analysis.

Which statistics definitions should you know?

What shortcuts save time on GRE statistics?

• Use the sum, not the list. Mean × count = sum. If five numbers average 12, they add up to 60, and you rarely need the numbers themselves.
• Adding a constant shifts the centre, not the spread. Add 10 to every value and the mean and median rise by 10, but the range and standard deviation do not change.
• Multiplying scales everything. Multiply every value by 3 and the mean, median, range and standard deviation are all multiplied by 3.
• Compare spread by eye. You will rarely calculate a standard deviation on the GRE. Usually you compare two lists: the one whose values sit further from its mean has the larger standard deviation.
• Mean versus median. A few very large values pull the mean above the median. A few very small values pull it below.

How does the normal distribution work on the GRE?

A normal distribution is the symmetric, bell-shaped curve. The mean, median and mode are all at the centre. The facts you need are the approximate shares of data within each band:

Because the curve is symmetric, half of each band sits on either side of the mean. So about 34% of the data lies between the mean and one standard deviation above it, and about 2.5% lies more than two standard deviations above it.

What are GRE Data Interpretation sets?

ETS describes a Data Interpretation set as a group of questions based on the same data, shown in tables, graphs or other displays. The questions can be in any of the four Quant formats. Three habits help:

• Read the titles, labels and units first. A bar chart in thousands and a table in percentages need different arithmetic.
• Estimate before you calculate. Many answer choices are far apart, so rounding is often enough to choose.
• Check whether the question asks for a value or a change. “Percent of” and “percent increase” give very different answers from the same chart.

GRE statistics practice questions with solutions

These five practice questions are written by Galvanize in the official GRE formats. Try each one before reading the solution.

Question 1 (numeric entry)

The mean of five numbers is 12. Four of the numbers are 10, 11, 14 and 15. What is the fifth number?

Answer: 10. The five numbers add up to 5 × 12 = 60. The four known numbers add up to 10 + 11 + 14 + 15 = 50, so the fifth is 60 − 50 = 10.

Question 2 (multiple choice, select one)

What is the median of the list 3, 8, 5, 12, 7, 9?

(A) 7   (B) 7.5   (C) 8   (D) 8.5   (E) 9

Answer: (B) 7.5. In order the list is 3, 5, 7, 8, 9, 12. There are six values, so the median is the mean of the third and fourth: (7 + 8) ÷ 2 = 7.5. Choice (D) comes from finding the middle without sorting the list first.

Question 3 (Quantitative Comparison)

List S: 2, 4, 6, 8, 10    List T: 12, 14, 16, 18, 20

Quantity A: the standard deviation of list S    Quantity B: the standard deviation of list T

(A) Quantity A is greater. (B) Quantity B is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given.

Answer: (C). Every value in T is the matching value in S plus 10. Adding a constant moves the whole list without changing how spread out it is, so the standard deviations are equal. No calculation is needed.

Question 4 (multiple choice, select one or more)

For the list 1, 3, 3, 5, 8, which of the following statements are true? Indicate all such statements.

(A) The mean is 4.   (B) The median is 4.   (C) The mode is 3.   (D) The range is 8.   (E) The mean is greater than the median.

Answer: (A), (C) and (E). The sum is 20 and there are five values, so the mean is 4: (A) is true. The median is the third value, 3, so (B) is false. 3 appears twice, so the mode is 3: (C) is true. The range is 8 − 1 = 7, so (D) is false. The mean of 4 is greater than the median of 3, pulled up by the 8: (E) is true.

Question 5 (multiple choice, select one)

Scores on a test are normally distributed with a mean of 150 and a standard deviation of 8. Approximately what percent of scores are above 166?

(A) 2.5%   (B) 5%   (C) 16%   (D) 34%   (E) 47.5%

Answer: (A) 2.5%. 166 is 16 above the mean, which is 2 standard deviations. About 95% of scores lie within 2 standard deviations of the mean, leaving about 5% outside, split equally between the two tails. So about 2.5% are above 166. Choice (B) forgets to split the 5% between the tails.

How should you practise GRE statistics?

• Learn the definitions exactly. Most errors come from a half-remembered rule, such as taking the median without sorting.
• Practise the shift and scale rules. They turn many Quantitative Comparison questions into one-line answers.
• Read real charts. News graphs and report tables are good practice for Data Interpretation: read the labels, then estimate.
• Practise under timing. At just over 1.7 minutes a question, Data Interpretation sets reward estimating over exact arithmetic.

To see how your data analysis holds up across the whole section, take the free GRE mock test. For more practice in every content area, try our GRE sample questions with answers. To turn a practice score into a target, use the GRE score calculator.

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