GRE Data Analysis: Concepts, Formulas & Practice Questions

GRE Data Analysis is one of the four content areas in the Quantitative Reasoning section of the GRE, alongside Arithmetic, Algebra, and Geometry. It tests descriptive statistics, graph and table interpretation, probability, distributions, and counting methods, and it rewards quick reasoning over long calculations.

In this guide, you will find the full GRE Data Analysis syllabus with formulas, preparation strategies, six practice questions with answers, and the traps that cost test-takers the most marks.

Key Highlights:

• GRE Data Analysis syllabus covers descriptive statistics, data interpretation, elementary probability, conditional probability, distributions, and counting methods.
• GRE Data Analysis formulas include rules for mean, median, standard deviation, probability, permutations, and combinations.
• GRE Data Analysis practice questions test your ability to interpret graphs and tables, compare quantities, and solve probability and counting problems under time pressure.

What is GRE Data Analysis?

 Data Analysis is one of the topics in GRE Quantitative Reasoning section that tests how well you describe, interpret, and conclude numerical data. Questions appear as standalone problems or as Data Interpretation sets, where several questions share one table or graph.

• Adaptive testing: The GRE test adapts at the section level. Your performance in the first Quantitative section decides the difficulty of the second, so accurate early answers on Data Analysis questions raise the level of what follows. 
• Question formats: GRE data analysis question formats include multiple choice (select one or more), numeric entry, and quantitative comparison, and the test provides an on-screen GRE calculator.

Expert Insight: Data Interpretation is a question format, while Data Analysis is the content area. A GRE Data Interpretation question can also borrow arithmetic or algebra skills, but the statistics, probability, and counting behind it come from Data Analysis.

GRE Data Analysis Syllabus

The GRE Data Analysis syllabus covers six key topic areas that test your ability to interpret data, analyse relationships, and solve quantitative problems. 

Descriptive Statistics 

 Descriptive statistics on the GRE cover the mean, median, mode, range, standard deviation, interquartile range, quartiles, and percentiles. The table below shows what each measure does and how it reacts to an outlier and to a change applied to every value in the list.

These four points explain how the measures behave in GRE Data Analysis questions.

• Mean versus median: The median acts as the halving point of the data, while the mean acts as its balance point. In the list 2, 3, 4, 5, 6, the mean and median both equal 4. Replace 6 with 60, and the mean rises to 14.8 while the median stays at 4.
• Weighted and combined means: When values repeat, multiply each value by its frequency, add the products, and divide by the total count. Two groups combine as (n1 × mean1 + n2 × mean2) divided by (n1 + n2).
• Standardisation: The number of standard deviations a value lies from the mean equals (value minus mean) divided by the standard deviation. Most values in any data set fall within about 3 standard deviations of the mean.
• Population versus sample standard deviation: The GRE Math Review divides by n, while the sample version divides by n minus 1. Expect questions on how standard deviation changes rather than longhand calculations.

1. Interpretation of Data in Tables and Graphs

GRE data interpretation questions use tables, bar graphs, line graphs, circle graphs, boxplots, scatterplots, and frequency distributions. Each display rewards a different reading habit, so the bullets below list what to extract from each.

• Frequency distributions: A frequency table lists each value with its count. Relative frequency equals the count divided by the total and always adds up to 100 per cent. A histogram shows the same data with touching bars on a number line.
• Bar graphs: Bar height shows the frequency or value. In a segmented bar, read a middle segment as its top edge minus its bottom edge, not as its height from the axis.
• Line graphs: Time sits on the horizontal axis. The steepest segment between consecutive points marks the biggest change, so compare slopes instead of heights.
• Circle graphs: Each sector’s angle equals its percentage of 360 degrees, so a 7 per cent sector spans 25.2 degrees. Two sectors from the same graph share one total, so their ratio equals the ratio of their percentages.
• Boxplots: A boxplot shows five numbers, namely the least value, Q1, the median, Q3, and the greatest value. The box length equals the interquartile range, which makes boxplots ideal for comparing spread between two data sets.
• Scatterplots: A scatterplot shows the relationship between two variables. The slope of the trend line gives the predicted change in the vertical variable for each unit change in the horizontal one, and a negative slope means the vertical variable falls as the horizontal one rises.
• Tables: Percentage columns often carry different totals in different years or groups. Convert a percentage to a count before you compare across columns.

2. Elementary Probability

Elementary probability questions in the GRE Data Analysis measure how likely an event is on a scale from 0 (impossible) to 1 (certain). It spans compound events and independent events, and four rules solve most questions.

• Basic probability: P(E) equals the number of favourable outcomes divided by the number of equally likely outcomes.
• Complement: P(not E) equals 1 minus P(E). Use this for any “at least one” question, because 1 minus the probability of none is usually the faster route.
• Either event: P(E or F) equals P(E) plus P(F) minus P(E and F). For mutually exclusive events, the last term equals zero, so you simply add.
• Independent events: P(E and F) equals P(E) × P(F). Rolling a fair die twice and getting a 3 both times has probability 1/6 × 1/6, which equals 1/36.

Two events with non-zero probabilities cannot be both mutually exclusive and independent. Mutually exclusive events cannot occur together, while independent events do not affect each other.

3. Conditional Probability

Conditional probability measures the chance of an event after another event has already occurred. It appears most often in draws without replacement and in two-way tables.

• Formula: P(B given A) equals P(A and B) divided by P(A).
• Draws without replacement: P(first and second) equals P(first) × P(second given first). A box with 3 red and 2 blue marbles gives P(both red) = 3/5 × 2/4 = 3/10.
• Two-way tables: The word “given” shrinks the denominator to the row or column named after it, so divide by that total and not by the grand total.
• Independence test: Events A and B are independent when P(B given A) equals P(B).

4. Random Variables and Probability Distributions

A random variable assigns a number to each outcome of a random experiment, and a probability distribution lists the probability of each value. The GRE tests discrete distributions in tables and the normal distribution in word descriptions.

• Probability distribution: The probabilities of all possible values always add up to 1.
• Expected value: The mean of a random variable equals the sum of each value multiplied by its probability. A variable that takes the values 0, 1, and 2 with probabilities 0.2, 0.5, and 0.3 has an expected value of 1.1.
• Normal distribution: The curve is bell-shaped and symmetric, and the mean, median, and mode coincide. About 68 per cent of values fall within 1 standard deviation of the mean, about 95 per cent within 2, and nearly all within 3.
• Effect of standard deviation: A smaller standard deviation gives a taller, narrower curve around the same mean.
• Symmetry shortcut: Exactly half the area lies above the mean, so P(X greater than the mean) equals 0.5.
• Standard normal distribution: It has a mean of 0 and a standard deviation of 1. You standardise any normal value by subtracting the mean and dividing by the standard deviation.

5. Counting Methods

Counting methods on the GRE cover the multiplication principle, permutations, combinations, and Venn diagrams. The deciding question in almost every problem is whether order matters.

• Multiplication principle: k choices followed by m independent choices give k × m outcomes.
• Factorial: n! equals n × (n minus 1) × ... × 1, and 0! equals 1.
• Permutations (order matters): The number of ways to select and order k items from n equals n! divided by (n minus k)!.
• Combinations (order does not matter): The number of ways to choose k items from n equals n! divided by k! (n minus k)!, and n choose k equals n choose (n minus k).
• Permutations versus combinations: From 6 candidates, ranking 2 of them gives 30 outcomes, while choosing 2 without ranking gives 15.
• Venn diagram with two sets: The count in A or B equals the count in A plus the count in B minus the count in both, which removes the double count.

GRE Data Analysis Practice Questions With Answers

Attempt each GRE Data Analysis question before checking the answer and aim to solve it within 1 minute and 45 seconds. This approach will help you assess your accuracy, identify weak areas, and improve your time management for the GRE. 

1. Descriptive Statistics Practice Question

This quantitative comparison question tests how an outlier moves the mean and the median. The skill is spotting the direction of the gap without heavy arithmetic.

Question: Set S contains the values 3, 5, 6, 8, and 40. Quantity A is the mean of S, and Quantity B is the median of S.

(A) Quantity A is greater. 

(B) Quantity B is greater.

(C) The two quantities are equal. 

(D) The relationship cannot be determined.

Answer: (A) Quantity A is greater.

Explanation: The mean equals 62 divided by 5, which is 12.4. The median is the middle value, 6. The outlier 40 pulls the mean above the median.

2. Data Interpretation Practice Question

This question tests per cent change from a table. The skill is separating the biggest per cent increase from the biggest absolute increase.

Question: Which program had the largest increase in applications from 2024 to 2025?

(A) Data Science
(B) Computer Science
(C) MBA
(D) All three increased by the same percent.

Answer: (A) Data Science.

Explanation: Data Science rose by 60 on a base of 200, which is 30 per cent. Computer Science rose by 80 on 800, which is 10 per cent. MBA rose by 60 on 500, which is 12 per cent. Computer Science has the largest absolute increase, but Data Science has the largest per cent increase.

3. Elementary Probability Practice Question

This numeric entry question tests the complement rule with independent draws. The skill is choosing 1 minus the probability of none over listing every favourable case.

Question: A bag holds 4 red marbles and 6 blue marbles. You draw one marble, replace it, and draw again. What is the probability that at least one marble is blue? Enter your answer as a fraction.

Answer: 21/25.

Explanation: P(both red) equals 4/10 × 4/10, which is 4/25. Subtract from 1 to get 1 minus 4/25, which equals 21/25.

4. Conditional Probability Practice Question

This question tests conditional probability from a two-way situation. The skill is choosing the correct denominator after the word “given”.

Question: Of 200 applicants, 120 submitted GRE scores. Of those 120, 30 received a scholarship. Of the 80 who did not submit GRE scores, 10 received a scholarship. If an applicant chosen at random received a scholarship, what is the probability that the applicant submitted GRE scores?

(A) ¼
(B) 3/10
(C) ½
(D) 3/4. 

Answer: (D) 3/4.

Explanation: The condition limits the pool to the 40 applicants who received a scholarship. Of these, 30 submitted GRE scores, so the probability equals 30/40, which is 3/4. Option (A) is the reverse probability of receiving a scholarship given a GRE submission (30/120).

5. Normal Distribution Practice Question

This question tests the 68% rule for a normal distribution. The skill is converting an interval into standard deviations from the mean.

Question: The time 2,000 students take to complete a mock Quantitative section is approximately normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes. How many students take 35 to 45 minutes?

(A) 680
(B) 1,000.
(C) 1,360
(D) 1,900. 

Answer: (C) 1,360.

Explanation: The values 35 and 45 lie exactly 1 standard deviation below and above the mean. About 68 per cent of the data fall in this range, and 68 per cent of 2,000 equals 1,360.

6. Counting Methods Practice Question

This numeric entry question tests combinations. The skill is recognising that equal awards mean order does not matter.

Question: A panel selects 3 of 7 finalists to receive identical awards. How many different groups of 3 finalists can the panel select?

Answer: 35.

Explanation: Order does not matter, so use 7!/(3! × 4!), which equals (7 × 6 × 5)/(3 × 2 × 1), or 210/6, which is 35. If the awards were ranked first, second, and third, the answer would be 210.

Common Traps in GRE Data Analysis

The most common traps in GRE Data Analysis involve misreading quantities, applying the wrong formula, or overlooking important details in a question. Recognising them can help you improve accuracy and save time during the exam.

• Per cent Versus Count: A percentage can rise even when the actual count falls if the total decreases. In the ETS airline example, flight-problem complaints increased from 20.0% to 22.1%, but the number of complaints fell because total complaints dropped from 22,998 to 13,278.
• Wrong Base for Percentage Change: Calculate percentage change by dividing the difference between the new and old values by the old value. For example, an increase from 400 to 500 represents a 25% rise, not 20%, because the original value provides the base for the calculation.
• Scale and Units: Always check the axis labels, column headings, and footnotes before interpreting a graph or table. If an axis uses billions, a bar at 5 represents 5 billion, not 5 units.
• Median of Combined Groups: You cannot determine the median of a combined dataset by simply averaging the medians of two groups. Even if the group medians are 80 and 72, you need the underlying values or additional information to establish the median of all 50 observations.
• Mutually Exclusive Versus Independent Events: Mutually exclusive events cannot occur together, whereas independent events do not affect each other's probabilities. Two mutually exclusive events with non-zero probabilities cannot also be independent.
• Ignoring Replacement in Probability: When you draw items without replacement, the second draw depends on the first because the available pool changes. Update both numerator and denominator when calculating the second probability.
• Permutation Versus Combination: Use permutations when the order of selection matters, such as when ranking candidates, arranging seating, or assigning distinct roles. Use combinations when selecting a group or committee, and the order does not matter.
• Constant Changes and Spread: Adding the same constant to every value leaves the range, interquartile range, and standard deviation unchanged. Multiplying every value by a constant changes these measures in proportion to the absolute value of that constant.
• Double Counting in Venn Diagrams: Adding the sizes of two overlapping sets counts their shared elements twice. Subtract the overlap once to calculate the total number of unique elements across both sets.

GRE Data Analysis Preparation Strategies

To prepare for GRE Data Analysis, learn the essential formulas first, then practise estimating the direction and approximate value of an answer before performing calculations. These strategies help you manage the 1 minute and 45 seconds available per question, improve accuracy, and avoid spending too much time on lengthy calculations.

• Start with official material: ETS Math Review Chapter 4 covers every syllabus topic and ends with 19 exercises with worked answers. ETS also offers free POWERPREP Online practice tests that mirror the real GRE interface.
• Predict before you calculate: Many questions ask whether the mean, median, or standard deviation rises, falls, or stays the same after a change. Write the direction first and calculate only when the answer choices stay close.
• Read the display once: In a Data Interpretation set, read the title, axis labels, units, and footnotes before you open the first question. Every question in the set reuses this information.
• Use Mark and Review: The GRE lets you skip a question, mark it, and return to it within the same section. Leave a long counting problem for later and solve the quicker questions first.
• Estimate before you use the calculator: Use the on-screen GRE calculator for complex arithmetic, but round percentages and other values to convenient numbers first. Estimation helps you eliminate unlikely answer choices quickly.
• Log every error by trap type: Use a GRE error log to tag each mistake as a unit error, wrong base, order confusion, or misread table. Review these patterns regularly to identify recurring weaknesses. 

From the Desk of Yocket

Most GRE data analysis topics like mean, median, standard deviation, permutations, combinations, and probability are taught in Class 11 and 12 mathematics. However, the GRE tests how quickly you can apply them to unfamiliar problems. Treat every Data Analysis question as a reading task first and a calculation task second, and the section becomes one of the most predictable parts of your GRE.

If you want to improve your GRE Quantitative Reasoning accuracy, Yocket Prep can help you practise question types, strengthen your problem-solving skills, and identify areas that need more work. Regular practice with timed questions can help you manage your time more effectively on test day.