GRE Data Analysis: Statistics, Probability and Interpretation

GRE Data Analysis is one of four content areas inside Quantitative Reasoning, alongside Arithmetic, Algebra and Geometry, according to ETS's official content overview. It groups statistics, counting methods, probability and data interpretation into one tested skill set. The GRE Math Review devotes a full chapter to this area, split into six sections: methods for presenting data, numerical methods for describing data, counting methods, probability, distributions of data and random variables, and data interpretation examples.

This guide works through each piece in order: descriptive statistics, counting principles, basic and compound probability, chart and table reading, multi-question Data Interpretation sets, and the traps built around weighted averages and mutually exclusive events. Every example here is original, built to mirror the reasoning tested on exam day without repeating an official question. Read it top to bottom once, then return to single sections while you drill.

What ETS Tests in Data Analysis

ETS's Math Review chapter four lists six sections under Data Analysis. This table matches each one to where this guide covers it. Five of the six map to a section below. Section 4.5, distributions of data and random variables, is a gap in this guide, so work through it in the official PDF.

Descriptive Statistics: Mean, Median, Mode, Range and Standard Deviation

Section 4.2 of the Math Review splits descriptive statistics into two groups: measures of central tendency (mean, median, mode) and measures of dispersion (range, interquartile range, standard deviation). Both groups describe a data set from a different angle: where its center sits, and how spread out its values are. The subsections below work through every measure using one shared data set.

Measures of Central Tendency

The mean is the sum of all values divided by the count of values. The median is the middle value once the data set is sorted, or the average of the two middle values when the count is even. The mode is the value appearing most often, and a data set is allowed to have no mode, one mode, or more than one.

Take eight quiz scores: 68, 72, 75, 75, 80, 85, 90, 95. The scores sum to 640, so the mean is 640 divided by 8, or 80. The two middle values are 75 and 80, so the median is 77.5. The score 75 appears twice while every other score appears once, so the mode is 75.

Measures of Dispersion

Range is the highest value minus the lowest value. For the quiz scores above, the range is 95 minus 68, or 27. Interquartile range narrows the focus to the middle half of the data, found by subtracting the first quartile from the third quartile, and it ignores extreme values at either end.

Standard deviation measures the typical distance between each value and the mean. A small standard deviation means values cluster close to the mean, and a large one means values spread out further. To find it, subtract the mean from every value, square each difference, average the squared differences, then take the square root of the result. The table below carries out this calculation for the eight quiz scores, where the mean is 80.

The squared deviations sum to 608. Dividing by 8 gives 76, and the square root of 76 rounds to about 8.72. GRE Quant questions on standard deviation usually ask you to compare spread rather than compute the value. A comparison question asks which of two data sets spreads out further, or which reacts more to a single outlier.

Counting Principles, Permutations and Combinations

Section 4.3 of the Math Review covers counting methods: sets, lists and techniques for finding how many outcomes exist without listing every one. Two tools handle standard GRE counting work: the fundamental counting principle, and the permutation and combination formulas. Both turn on one question, whether the order of a selection changes the result.

The Fundamental Counting Principle

The fundamental counting principle states the total number of outcomes across several independent choices equals the product of the number of options at each stage. Multiply, do not add, when the choices happen in sequence and each combination counts as a distinct outcome. Take a student picking one shirt from 4 options, one pair of pants from 3 options, and one pair of shoes from 2 options. The total number of outfits equals 4 times 3 times 2, or 24.

Permutations vs Combinations

A permutation counts arrangements where order matters, and a combination counts selections where order does not matter. Both start from the same idea, picking r items from a group of n, and differ only in whether the order of the pick changes the outcome. The two formulas below follow from this single difference.

• Permutation: nPr equals n factorial divided by (n minus r) factorial.
• Combination: nCr equals n factorial divided by r factorial times (n minus r) factorial.

A club with 5 members elects a president and a secretary. Order matters here, since the two roles differ, so this is a permutation: 5P2 equals 5 times 4, or 20 possible outcomes. The same club instead picks a 2-person committee, where order does not matter, so this is a combination: 5C2 equals 10 possible committees. The table below separates the two by whether order changes the count.

Basic and Compound Probability

Section 4.4 of the Math Review defines probability as a number between 0 and 1, describing the sample space and events on which every probability question builds. The official content overview adds compound events, independent events and conditional probability on top of this foundation. The two subsections below take single events first, then combinations of events.

Single-Event Probability

Probability equals the number of favorable outcomes divided by the total number of possible outcomes. A probability of 0 means an event never happens, and a probability of 1 means it always happens. Take a bag holding 4 red marbles and 6 blue marbles, 10 marbles in total. The probability of drawing a red marble equals 4 divided by 10, or 0.4.

Compound, Independent and Conditional Probability

A compound event combines two or more single events. Two events are independent when the outcome of one has no effect on the other, and the probability of both independent events happening equals the product of their individual probabilities. Rolling two dice, the probability both land on 6 equals 1/6 times 1/6, or 1/36, since one roll has no effect on the other.

Conditional probability describes the probability of an event given another event already happened. Drawing without replacement changes the total for the second draw, since one item is already removed from the group. Take a deck of 5 cards holding 3 red cards and 2 blue cards: drawing two cards without replacement, the probability the first card is red and the second card is also red equals 3/5 times 2/4, or 3/10, since only 4 cards and 2 red cards remain for the second draw.

Reading Charts, Tables and Graphs

Section 4.1 of the Math Review covers methods for presenting data, the formats the GRE uses to display information in Data Interpretation sets. Common formats include bar graphs, circle graphs, line graphs, tables and scatterplots. Reading the display correctly before doing any math prevents avoidable errors. Work through each display in the order below.

1. Read the title first, since it states what the entire display measures.
2. Check every axis label and unit, since a chart in thousands of dollars reads differently from one in millions.
3. Note the scale, since some charts start above zero or skip values, which changes how differences look.
4. Check the legend on any chart with more than one data series, since colors or patterns are not always labeled inside the plotted area.
5. Compute only the value asked for in the question, since a display holds far more information than any single question needs.

Multi-Question Data Interpretation Set Strategy

Data Interpretation questions are grouped together and refer to the same table, graph or other data presentation, per ETS's official overview. Each question in the set draws on the same shared display, and ETS states the question types inside a set draw from Multiple-choice select one, Multiple-choice select one or more, or Numeric Entry, the same formats used across GRE Quant minus Quantitative Comparison. ETS does not publish a fixed number of questions per Data Interpretation set on its official pages, so check the current Quantitative Reasoning overview for the latest structure before test day. The steps below hold for a set of any size.

1. Read the shared chart or table once before opening the first question, so the layout is already familiar by the second and third question.
2. Note every unit and scale on the display, since a single missed unit throws off every question built on it.
3. Answer only what the current question asks, since Data Interpretation sets often include a value calculated for one question but not needed by the next.
4. For Multiple-choice select one or more, check every option against the display individually, since partial credit does not exist for this format.
5. For Numeric Entry, follow the stated form exactly, whether a whole number, a decimal or a percent.

Common Traps: Weighted Averages and Mutually Exclusive Events

Two setups produce wrong answers even when the arithmetic is clean: weighted averages and mutually exclusive events. Both fail the same way, by borrowing the rule from a neighboring concept. A weighted average gets treated as a plain average, and mutually exclusive events get treated as independent events. Each subsection below states the correct rule first, then the reversal to watch for.

Weighted Average Traps

A weighted average accounts for group size, and combining two averages by adding them together and dividing by 2 works only when both groups are the same size. When group sizes differ, the average with more members pulls the combined average toward it. Take a class of 20 students averaging 80 on a test and a class of 30 students averaging 90. The plain average of 80 and 90 is 85, but the true combined average weights each score by its group size: 20 times 80 plus 30 times 90, divided by 50 total students, equals 4,300 divided by 50, or 86.

Mutually Exclusive vs Independent Events

Two events are mutually exclusive when they cannot happen at the same time, and the probability of one or the other happening equals the sum of their individual probabilities. Two events are independent when one has no effect on the other, and the probability of both happening equals the product of their individual probabilities. One rule adds, the other multiplies.

A bag holds red, blue and green marbles. Drawing red or blue is mutually exclusive, since a single marble is not both colors, so the probability of red or blue equals the probability of red plus the probability of blue. Rolling two separate dice is independent, since the first roll does not affect the second, so the probability of two particular results equals the product of their individual probabilities, as shown in the dice example above. The trap reverses these rules: adding probabilities for independent events, or multiplying probabilities for mutually exclusive events, produces the wrong answer every time.

Our free Data Analysis drills split practice into three matched sets, descriptive statistics, counting and probability, and data interpretation, each across three difficulty levels. Practice is free and needs no signup on our GRE practice page. Pair this guide with our GRE Quant Reasoning overview covering all four content areas, our GRE integers, fractions and exponents guide for the arithmetic side of Quant, and our GRE score calculator to see how a stronger Data Analysis section moves your Quant score.

Sources

• ETS: GRE Quantitative Reasoning Content Overview
• ETS: GRE Math Review (PDF)