GRE Multiple Choice (Select One): Data Analysis Questions

Data Analysis is one of the four content domains tested in GRE Quantitative Reasoning. It spans statistics, probability, counting methods, normal distributions, and interpretation of tables and graphs. In the Multiple Choice Select One format, you see five answer choices displayed as radio buttons and must pick exactly one. These questions range from straightforward probability computations to multi-step problems that combine conditional probability with Venn diagrams or require careful case-based counting. Below you will learn the six question patterns that appear, work through two interactive examples step by step, and then practice with six guided questions drawn from a calibrated question bank.

What Are MC Select One Data Analysis Questions?

Data Analysis MC Select One questions test your ability to work with statistics, probability, counting, and data interpretation. You are given a problem involving data, presented with five answer choices labeled A through E displayed as radio buttons, and you must select exactly one correct answer. These questions cover mean, median, mode, range, standard deviation, probability (basic, compound, and conditional), combinations, permutations, normal distribution concepts, and interpretation of tables, graphs, and charts.

Many Data Analysis questions appear as part of Data Interpretation sets, where two to five questions share a common data display such as a table, bar graph, line graph, or circle graph. However, standalone Data Analysis questions are also common, especially those testing probability, counting, and statistical properties. The difficulty ranges from straightforward single-step problems to multi-step challenges that combine several concepts.

Frequency note: Data Analysis accounts for approximately 25% of all GRE Quantitative Reasoning questions. You can expect 8 to 12 Data Analysis questions across both quant sections, making this one of the most heavily tested domains. The questions that combine probability with counting or require the 68-95-99.7 rule tend to land at Medium to Hard difficulty.

6 Patterns You'll See

Nearly every MC Select One Data Analysis question falls into one of six patterns. Recognizing the pattern quickly tells you which formula or strategy to apply.

Probability Calculation

Compute a probability from given conditions. This includes complement counting (

1 - P

), the multiplication rule for independent events, conditional probability, and sampling without replacement. Look for phrases like "what is the probability that" or "closest to the probability."

Combination and Permutation Counting

Determine how many ways to choose or arrange items. Combinations (

\binom{n}{r}

) apply when order does not matter, such as selecting a committee. Permutations (

P(n,r)

) apply when order matters. The GRE heavily favors combinations. Watch for "how many" or "how many different" in the stem.

Standard Deviation Properties

Questions that test your understanding of how transformations affect standard deviation. Adding a constant shifts the mean but does not change the SD. Multiplying by a constant

k

scales the SD by

|k|

. These are conceptual questions that require no heavy computation.

Percent-of-Total and Venn Diagrams

Determine what percent or fraction of a group satisfies a condition, often using Venn diagram logic (inclusion-exclusion). The formula

|A \cup B| = |A| + |B| - |A \cap B|

is essential. Watch for "what percent of the group are" or "how many are in neither."

Mean, Median, and Central Tendency

Compute the mean or median from a frequency distribution or data table. For median with an even count of values, remember to average the two middle values. For the mean, compute the weighted sum divided by the total count.

Normal Distribution (68-95-99.7 Rule)

Determine the approximate percentage of values within a given range using the empirical rule. Convert bounds to z-scores, then combine the known percentages: 68% within 1 SD, 95% within 2 SD, 99.7% within 3 SD of the mean.

How to Solve Data Analysis Questions

These seven strategies apply across all six patterns. Work through them in order and you will avoid the most common errors.

Before answering any question about a data display, read the title, axis labels, and units. Identify the scale: is the data in thousands, millions, or billions? Note whether the graph shows totals, percentages, or rates. Misreading the scale is one of the most common errors on Data Interpretation questions.

When the question says "approximately" or "closest to," you do not need exact values. Round to make arithmetic easier. For example, $5.8 billion becomes roughly $6 billion, and 29.7% becomes roughly 30%. Eliminate choices that are clearly too far from your estimate before doing any detailed calculation.

When asked "what is the probability that event X does NOT happen," compute $P(\text{not } X) = 1 - P(X)$ . This is especially useful when $P(X)$ is easier to compute than $P(\text{not } X)$ directly. For example, to find the probability that at least one event occurs, compute 1 minus the probability that none occur.

For "how many ways to choose $k$ from $n$ ," use $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ . Key shortcuts: $\binom{n}{1} = n$ , $\binom{n}{n-1} = n$ (choosing what to leave out), and $\binom{n}{2} = \frac{n(n-1)}{2}$ . These shortcuts save time and reduce errors on the GRE.

Adding or subtracting a constant to every value shifts the mean but does not change the standard deviation. Multiplying every value by a constant $k$ multiplies the standard deviation by $|k|$ . Standard deviation measures spread, not location.

For two-set Venn diagram problems, use $|A \cup B| = |A| + |B| - |A \cap B|$ . For three sets, add back the triple intersection: $|A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C|$ . The "neither" count equals Total minus $|A \cup B|$ .

When selecting multiple items from a group without replacement, the second probability uses a reduced denominator. For example, if selecting 2 from 700 where 580 are non-lawyers: P(both non-lawyers) = $\frac{580}{700} \times \frac{579}{699}$ , not $\left(\frac{580}{700}\right)^2$ . The word "without replacement" or the physical setup (drawing cards, selecting people) signals this adjustment.

Pro tip: Before computing, identify which pattern the question falls into. If you can name the pattern within 10 seconds, you already know which formula to reach for. This recognition saves 30 to 60 seconds per question on test day.

Worked Example: Reading a Bar Chart

Work through each step below. You must answer each mini-challenge correctly to unlock the next step. If you get stuck, a second wrong attempt will reveal the answer so you can keep going.

Interactive Walkthrough0/4 steps

Reading a Bar Chart

The bar chart below shows the number of books sold by a bookstore during each month from January through June.

By what percent did sales increase from February to April?

Step 1: Read the February value

From the chart, how many books were sold in February?

Step 2: Read the April value

Step 3: Compute percent increase

Step 4: Identify the trap

Worked Example: Mean from a Frequency Table

This example teaches how to compute a weighted mean from a frequency distribution and avoid the common trap of simply averaging the score values.

Interactive Walkthrough0/4 steps

Mean from a Frequency Table

The table below shows the distribution of scores on a 5-point quiz for a class of 30 students.

Score	1	2	3	4	5
Frequency	2	4	9	10	5

What is the mean score for the class?

Step 1: Compute weighted sum

1(2) + 2(4) + 3(9) + 4(10) + 5(5) = \,?

Step 2: Verify total frequency

Step 3: Compute the mean

Step 4: Identify the trap

Practice Questions

Now apply what you have learned. Each question has a step-by-step solution walkthrough. After you submit your answer, click through the solution one step at a time to compare against your own work.

Question 1 — Conditional Probability (Bayes' Theorem)

A company has three divisions. Division X has 200 employees, of whom 40 percent hold graduate degrees. Division Y has 300 employees, of whom 30 percent hold graduate degrees. Division Z has 500 employees, of whom 20 percent hold graduate degrees. If an employee selected at random from the entire company holds a graduate degree, what is the probability that the employee is from Division Z?

Question 2 — Combinations with Constraints

A committee of 5 people is to be selected from a group of 6 men and 5 women. If the committee must include at least 2 men and at least 2 women, how many different committees are possible?

Question 3 — Expected Value

A box contains 10 slips of paper, numbered 1 through 10. Two slips are drawn at random without replacement. A player wins a number of dollars equal to the positive difference between the numbers on the two slips drawn. What is the expected value of the player's winnings?

Question 4 — Normal Distribution (68-95-99.7 Rule)

The scores on a certain aptitude test are normally distributed with a mean of 72 and a standard deviation of 6. Approximately what percent of test-takers scored between 60 and 78?

Question 5 — Standard Deviation Under Transformation

A data set of

n

values has mean 40 and standard deviation 12. Each value

x

is first standardized using

y = \frac{x - 40}{12}

, and then rescaled using

z = 20y + 100

. What is the standard deviation of the resulting

z

-values?

Question 6 — Three-Set Inclusion-Exclusion

In a group of 80 tourists, 50 visited Museum A, 40 visited Museum B, and 30 visited Museum C. Exactly 20 visited both A and B, 15 visited both A and C, and 10 visited both B and C. If every tourist visited at least one museum, how many tourists visited all three museums?

Common Traps

Trap 1 — Forgetting "without replacement." When selecting 2 items from a group without replacement, the second probability uses a reduced denominator.

P(\text{both non-lawyers}) = \frac{580}{700} \times \frac{579}{699}

, not

\left(\frac{580}{700}\right)^2

. If the problem says "selected at random" from a finite group, the default is without replacement unless stated otherwise.

Trap 2 — Confusing "probability of X given Y" with "probability of Y given X." Conditional probability has a direction.

P(\text{grad} \mid Z)

is not the same as

P(Z \mid \text{grad})

. If a question asks for the probability that a graduate-degree holder is from Division Z, you need

P(Z \mid \text{grad}) = \frac{\text{grad in Z}}{\text{total grad}}

, not

\frac{\text{grad in Z}}{\text{total in Z}}

Trap 3 — Counting the wrong pool in combinations. When some members are already chosen, you must reduce both the pool and the number of spots. If 3 of 11 candidates are already on a 6-person team, you choose 3 more from the remaining 8, not from 11 or from 6. The answer is

\binom{8}{3} = 56

, not

\binom{11}{6} = 462

Recognizing Data Analysis Patterns

Use this table to quickly identify which strategy to apply based on the question stem. Pattern recognition is the fastest way to save time on test day.

Question Stem Signal	Pattern	Strategy to Apply
"What is the probability that..."	Probability	Complement rule, multiplication rule, or conditional probability
"How many combinations / arrangements..."	Counting	$\binom{n}{k}$ or $P(n,k)$ formula; identify pool and slots
"What is the standard deviation of..."	SD Properties	Adding constant: SD unchanged. Multiplying by $k$ : $\text{SD} \times \|k\|$
"What percent of the group..."	Venn / Percent	Inclusion-exclusion formula; draw a Venn diagram
"What is the mean / median..."	Central Tendency	Weighted sum / total; for median, find the middle value(s)
"Approximately what percent... normally distributed"	Normal Distribution	Convert to z-scores; apply 68-95-99.7 rule
"Closest to the probability that neither..."	Probability (complement)	P(neither) = P(not 1st) * P(not 2nd \| not 1st); estimate and match
"If every value is multiplied by k..."	SD Transformation	New SD = $\|k\| \times$ old SD; new mean = $k \times$ old mean + constant

The key to speed on Data Analysis questions is recognizing the pattern within the first 10 seconds. Once you know the pattern, the formula and strategy follow automatically. Practice categorizing questions before solving them, and you will notice a significant improvement in your pacing.

Study Checklist

MC Select One Data Analysis Mastery Checklist0/9 complete

Frequently Asked Questions

What topics fall under Data Analysis on the GRE?

Data Analysis on the GRE covers statistics (mean, median, mode, range, standard deviation), probability (basic, compound, and conditional), counting methods (combinations and permutations), normal distribution, and interpretation of tables, graphs, and charts. It is one of the four content domains alongside Arithmetic, Algebra, and Geometry.

How many Data Analysis questions appear on the GRE?

Data Analysis typically accounts for roughly 25% of the Quantitative Reasoning section. Across both quant sections you can expect 8 to 12 questions that involve data analysis concepts, including standalone problems and data interpretation sets. The exact count varies by test form, but Data Analysis is consistently one of the most heavily tested domains.

What is the difference between combinations and permutations on the GRE?

Combinations ( $\binom{n}{r}$ ) count the number of ways to choose items when order does not matter, such as selecting a committee. Permutations ( $P(n,r)$ ) count arrangements where order matters, such as assigning ranked positions. Use $\binom{n}{r} = \frac{n!}{r!(n-r)!}$ for combinations and $P(n,r) = \frac{n!}{(n-r)!}$ for permutations. The GRE most commonly tests combinations, so master the combination formula first.

Does adding a constant to every value change the standard deviation?

No. Adding or subtracting the same constant to every value in a data set shifts the mean but does not change the standard deviation. This is because standard deviation measures the spread of values around the mean, and when every value shifts by the same amount, all deviations from the mean remain identical. However, multiplying every value by a constant k does multiply the standard deviation by $|k|$ .

How should I handle "closest to" or "approximately" questions on the GRE?

When a question uses "closest to" or "approximately," you do not need exact values. Round numbers to make arithmetic easier, compute a rough estimate, and then choose the answer choice nearest to your estimate. For instance, (580/700)^2 is roughly (0.83)^2 = 0.69, which is closest to 0.7. Eliminate choices that are clearly too far away before doing any detailed work. This estimation approach can save 30 to 60 seconds per question.