GRE Data Analysis Practice Test Practice Questions with Answers

Approximately 30% of the GRE Quantitative Reasoning section focuses on data analysis, requiring a strong grasp of statistics and probability. Success on the GRE Data Analysis Practice Test depends on your ability to interpret graphs, analyze sets of numbers, and apply counting methods to solve complex problems. This section of the exam evaluates how effectively you can synthesize information from tables, bar charts, and frequency distributions to draw logical conclusions. By engaging with high-quality practice materials, such as those found in our GRE Prep hub, you can develop the pattern recognition skills necessary to handle even the most challenging data sets.

Concept Explanation

GRE Data Analysis is the study of interpreting, summarizing, and drawing inferences from data sets through statistical measures and probability theory. This domain encompasses several sub-topics, including descriptive statistics (mean, median, mode, range, and standard deviation), interpretation of data presented in various graphical formats, and the calculation of probabilities for independent or dependent events. To excel, you must understand the properties of the Normal Distribution, which often appears in standardized testing to describe how data points cluster around a central mean. Additionally, you will encounter counting problems involving permutations and combinations, where the order of selection determines which mathematical approach to use. Effectively using tools like an AI Question Generator can help you simulate the variety of data types you will see on test day, from box plots to scatterplots. Mastery of these concepts ensures you can quickly identify the relevant data within a larger table and ignore extraneous information designed to distract you.

Solved Examples

1. Measures of Central Tendency: A set of five integers has a mean of 12 and a median of 10. If the smallest integer is 6 and the largest is 20, what is the sum of the remaining two integers?

   1. Calculate the total sum of the five integers using the mean: $$12 \times 5 = 60$$

   2. Let the five integers be $a, b, c, d, e$ in ascending order. We know $a = 6, c = 10, e = 20$.

   3. The sum of the known integers is $6 + 10 + 20 = 36$.

   4. Subtract this from the total sum: $60 - 36 = 24$.

   5. The sum of the two remaining integers ($b$ and $d$) is 24.

2. Probability: A bag contains 4 red marbles and 6 blue marbles. If two marbles are chosen at random without replacement, what is the probability that both are red?

   1. Find the probability of the first marble being red: $\frac{4}{10} = \frac{2}{5}$.

   2. After taking one red marble, 3 red and 6 blue marbles remain (9 total).

   3. Find the probability of the second marble being red: $\frac{3}{9} = \frac{1}{3}$.

   4. Multiply the probabilities: $\frac{2}{5} \times \frac{1}{3} = \frac{2}{15}$.

3. Standard Deviation: Set X consists of the numbers {10, 20, 30}. Set Y consists of the numbers {110, 120, 130}. Which set has a larger standard deviation?

   1. Recall that standard deviation measures the spread of data points from the mean.

   2. Calculate the mean of Set X: $(10+20+30)/3 = 20$. The differences from the mean are -10, 0, and 10.

   3. Calculate the mean of Set Y: $(110+120+130)/3 = 120$. The differences from the mean are -10, 0, and 10.

   4. Since the distances from the mean are identical for both sets, the standard deviations are equal.

Practice Questions

1. The average (arithmetic mean) of seven numbers is 14. If the sum of six of these numbers is 82, what is the seventh number?

2. A committee of 3 people is to be chosen from a group of 7 candidates. How many different committees are possible?

3. In a group of 50 students, 28 are taking Spanish, 15 are taking French, and 8 are taking both. How many students are taking neither Spanish nor French?

4. The test scores for a class are normally distributed with a mean of 75 and a standard deviation of 5. Approximately what percentage of the class scored between 70 and 85?

5. If the range of a set of 10 integers is 25 and the smallest integer is -5, what is the largest integer in the set?

6. A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is exactly 5?

7. A data set contains the values {4, 8, 8, 12, 15, 15, 15, 20}. What is the median of this data set?

8. If the ratio of men to women in a room is 3:5 and there are 40 people in total, how many women are in the room?

Answers & Explanations

1. Answer: 16. The total sum of seven numbers is $14 \times 7 = 98$. Subtracting the sum of the first six numbers (82) from the total gives $98 - 82 = 16$.

2. Answer: 35. Since the order of people in a committee does not matter, use the combination formula: $$\binom{n}{k} = \frac{7!}{3!(7-3)!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$$

3. Answer: 15. Using the principle of inclusion-exclusion, the number of students taking at least one language is $28 + 15 - 8 = 35$. The number taking neither is $50 - 35 = 15$.

4. Answer: 81.5%. A score of 70 is 1 standard deviation below the mean, and 85 is 2 standard deviations above. In a normal distribution, ~34% falls between the mean and -1 SD, and ~47.5% falls between the mean and +2 SD. Total: $34 + 47.5 = 81.5$.

5. Answer: 20. Range is defined as the difference between the maximum and minimum values: $\text{Range} = \text{Max} - \text{Min}$. Thus, $25 = \text{Max} - (-5)$, which simplifies to $25 = \text{Max} + 5$, so $\text{Max} = 20$.

6. Answer: 1/9. There are $6 \times 6 = 36$ total outcomes. The pairs that sum to 5 are (1,4), (2,3), (3,2), and (4,1). There are 4 such pairs. Probability = $4/36 = 1/9$.

7. Answer: 13.5. With 8 values (an even number), the median is the average of the 4th and 5th values. The 4th value is 12 and the 5th value is 15. $(12 + 15) / 2 = 13.5$.

8. Answer: 25. The total parts in the ratio are $3 + 5 = 8$. Each part represents $40 / 8 = 5$ people. The number of women is $5 \times 5 = 25$.

1. If a data set has a standard deviation of 0, what must be true about the data?

• AAll values are zero
• BThe mean is zero
• CAll values in the set are identical
• DThe range is equal to the mean

Frequently Asked Questions

How is standard deviation tested on the GRE?

The GRE rarely asks you to calculate the exact standard deviation. Instead, it tests your conceptual understanding of how data spread affects the value and how adding or multiplying constants to a data set changes the deviation.

What is the difference between combinations and permutations?

In permutations, the order of selection matters (like a race where rank is important), whereas in combinations, the order does not matter (like choosing a group of friends for a trip). You can practice these distinctions using our AI Exam Simulator.

How do I handle boxplots on the GRE?

Boxplots divide data into four quartiles. You should be able to identify the minimum, first quartile, median (second quartile), third quartile, and maximum value from the visual representation.

Are calculators allowed for the Data Analysis section?

Yes, an on-screen calculator is provided during the GRE Quantitative Reasoning section. However, it is best used for basic arithmetic rather than complex statistical functions which are not available.

What is the "Normal Distribution" rule to remember?

You should memorize the 68-95-99.7 rule, which states that approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three. This is essential for solving many quantitative comparison style data questions.

Ready to improve your GRE score?

Practice with AI-powered GRE questions, personalized quizzes, adaptive learning, and detailed explanations.

Start GRE Prep Free