Data Analysis

Last updated July 07, 2026 · Reviewed by the AnvayaPrep team

Introduction

Data Analysis is the statistics and probability domain of GRE Quantitative Reasoning, spanning 36 topics that cover descriptive statistics, data visualization, probability, and counting techniques. The unit covers: measures of central tendency (mean, median, mode, weighted average), measures of spread (range, standard deviation, interquartile range), data visualization types (bar graphs, line graphs, pie charts, histograms, scatterplots, box plots, frequency tables, data tables), probability (basic probability, complement rule, independent and dependent events, conditional probability, overlapping events, expected value), counting methods (combinations, permutations, counting principle), and data interpretation traps. Data Analysis constitutes approximately 25% of the Quantitative Reasoning section and appears in two formats: standalone calculation questions and multi-question data interpretation sets based on a shared table or graph.

The GRE tests data analysis at a conceptual level more than a computational one. Knowing the formula for standard deviation is less important than knowing how standard deviation changes when data points are shifted or when an outlier is added. Knowing how to compute combinations is less important than recognizing when a problem requires combinations versus permutations. The highest-yield investment in this unit is developing reliable pattern recognition for what each question type requires.

Learning Objectives

• Calculate mean, median, mode, and range from a dataset, and predict how each changes when data points are added, removed, or modified
• Compute weighted averages and recognize the distinction between simple and weighted means
• Compare standard deviations of different datasets conceptually (without full computation) by identifying how spread out the data is around the mean
• Interpret quartiles, interquartile range, and box plots, and use them to answer questions about data distribution
• Read and extract information accurately from bar graphs, line graphs, pie charts, histograms, scatterplots, data tables, and frequency tables
• Identify the percent change between values shown in a data set or chart, using the original value as the denominator
• Apply the fundamental probability formula: P(event) = favorable outcomes / total outcomes
• Use the complement rule: P(event) = 1 - P(not event), especially for "at least one" problems
• Distinguish independent events (multiply probabilities) from dependent events (adjust for sampling without replacement)
• Apply the addition rule for overlapping events: P(A or B) = P(A) + P(B) - P(A and B)
• Apply combinations (n choose r = n! / (r!(n-r)!) when order does not matter and permutations (n! / (n-r)!) when order does matter
• Recognize and avoid the common data traps: wrong base for percent change, confusing median with mean, misreading graph scales

High-Yield Concepts

Measures of Central Tendency

The mean (arithmetic average) is sum divided by count. Its most important algebraic rearrangement: total sum = mean x count. This allows you to find a missing value when the mean and all other values are given, and to compare totals across groups. When a new data point is added, the new mean can be computed as (old sum + new value) / (old count + 1).

The median is the middle value in a sorted dataset. For an odd number of values, it is the middle element. For an even number, it is the average of the two middle elements. The median is not affected by extreme outliers; the mean is pulled toward outliers. The GRE tests this distinction directly.

Weighted average: when groups have different sizes, the overall mean is not the simple average of group means. Weight each mean by its group's size: weighted average = (sum of (group mean x group size)) / total size. The GRE consistently tests whether students apply equal weighting when unequal weighting is required.

Standard Deviation and Spread

Standard deviation measures how far data points are, on average, from the mean. The GRE does not require computing standard deviation from scratch; it tests conceptual effects.

Key rules: (1) Adding or subtracting a constant from every data point shifts the mean but does not change the standard deviation -- the spread remains identical. (2) Multiplying every data point by a constant multiplies the standard deviation by that constant. (3) Adding a data point equal to the mean decreases or maintains the standard deviation (the new point adds no spread). (4) Adding a data point far from the mean increases the standard deviation.

To compare standard deviations of two sets without computing: the set whose data points are more tightly clustered around its mean has the smaller standard deviation. {1, 2, 3, 4, 5} and {1, 1, 3, 5, 5} have the same mean (3) but the second set has larger standard deviation because the extreme values (1 and 5) appear more frequently.

Probability: The Core Rules

All probability values fall between 0 and 1 inclusive. A computed probability outside this range signals an error.

The complement rule: P(event) = 1 - P(event does not occur). This is the fastest method for "at least one" problems: P(at least one success) = 1 - P(no successes in any attempt).

Independent events (one outcome does not affect the other): P(A and B) = P(A) x P(B). Dependent events (one outcome affects the other): P(A and B) = P(A) x P(B|A), where P(B|A) is the probability of B given A already occurred. In sampling without replacement, the denominator changes for each successive draw.

The addition rule for overlapping events: P(A or B) = P(A) + P(B) - P(A and B). Without the subtraction, the overlapping region is counted twice.

Combinations vs. Permutations

Combinations count the number of ways to choose r items from n items when order does not matter: n! / (r!(n-r)!). Permutations count the arrangements when order does matter: n! / (n-r)!.

The determining question: does the order of selection matter? Choosing 3 people for a committee where all three have the same role is a combination (order doesn't matter). Choosing a president, vice president, and secretary from 3 people is a permutation (the specific person assigned to each role matters).

Permutations always produce a larger number than combinations for the same n and r because each combination corresponds to multiple permutations (specifically, r! permutations per combination).

Study Strategy

Begin with mean, median, and mode -- these are the most frequently tested statistics concepts and the foundation for all other data analysis. Master the weighted average formula early since it appears in a significant fraction of data analysis questions.

Study standard deviation conceptually (not computationally) alongside mean, since the GRE tests standard deviation effects rather than calculations.

Move to data visualization: practice reading each graph type (bar, line, pie, histogram, box plot, scatter) until you can extract numerical values and identify trends quickly. Data interpretation questions are time-intensive but reliable point sources once the graph-reading skill is fast.

Study probability rules as a single block: basic probability, complement rule, independent events, dependent events, and the addition rule. These build sequentially, and the complement rule in particular needs to become reflexive for "at least one" problems.

Complete the unit with counting methods (combinations and permutations). These are the most formula-dependent topics in the unit and the least frequently tested, so study them after securing the higher-frequency topics.

Common Mistakes

Averaging averages without weighting. When combining groups of different sizes, each group's mean must be weighted by its size. Simple averaging of group means is correct only when all groups are equal in size.

Using the new value instead of the original value as the denominator for percent change. Percent change in a statistic (such as the mean increasing from 40 to 50) is always (50-40)/40 = 25%, not (50-40)/50 = 20%.

Confusing "and" and "or" in probability problems. "And" (both events occur) means multiply probabilities (for independent events). "Or" (at least one occurs) requires the addition rule with subtraction of the overlap.

Forgetting to adjust denominators for dependent events. When selecting without replacement, each successive selection reduces the total number of items. P(second item is red | first item was red) has a denominator one less than the original total.

Choosing permutations when the problem calls for combinations. If the question asks about selecting a group or committee without distinct roles, use combinations. If positions or ranks are assigned, use permutations.

Misidentifying the median in an even-count dataset. For an even number of values, the median is the average of the two middle values, not either middle value alone.

Exam Tips

On data interpretation questions, read the graph title, axis labels, and unit descriptors before answering any question. GRE data traps frequently involve hidden unit differences (thousands vs. millions) or two different scales on the same chart.

Mean equals total sum divided by count. Rearranging: total = mean x count. Use this form when you need to find the sum from a given mean, or when comparing totals across datasets with different counts.

For probability questions involving "at least one," compute 1 minus P(none) rather than summing all the partial probabilities. This reduces a multi-term calculation to a single computation.

For any data table question where multiple percent changes are calculated, re-identify the original value (the earlier, starting value) for each individual calculation. Do not reuse a previous question's reference value.

When comparing standard deviations, visualize the datasets on a number line. The one whose values cluster closer to its mean has the smaller standard deviation, regardless of the mean's location.