GRE Data Analysis Exam Questions Practice Questions with Answers

Concept Explanation

GRE Data Analysis exam questions evaluate your ability to interpret, analyze, and synthesize data presented in various formats such as tables, bar graphs, line graphs, and circle graphs. This section of the GRE Quantitative Reasoning measure focuses on descriptive statistics, probability, and counting methods. To succeed, you must move beyond basic arithmetic and apply logical reasoning to identify trends, calculate percent changes, and determine the likelihood of specific outcomes. Understanding the distinction between discrete and continuous data is essential, as is the ability to handle large datasets using measures of central tendency like mean, median, and mode, as well as measures of dispersion like range and standard deviation. According to ETS, the creators of the GRE, these skills are fundamental to graduate-level research across most disciplines. For a structured approach to all quantitative sections, visiting a comprehensive GRE Prep hub can provide the necessary foundation. You might also find that using an AI Question Generator helps in creating personalized sets that target your specific weaknesses in data interpretation.

Solved Examples

1. Example 1: Percent Increase
   In 2020, a company had a revenue of $400,000. In 2021, the revenue increased to $520,000. What was the percent increase in revenue?
   
   1. Identify the initial value: $400,000.
   2. Find the amount of change: $520,000 - 400,000 = 120,000$.
   3. Divide the change by the initial value: $\frac{120,000}{400,000} = 0.3$.
   4. Multiply by 100 to get the percentage: $0.3 \times 100 = 30\%$.
2. Example 2: Probability of Independent Events
   A bag contains 4 red marbles and 6 blue marbles. If two marbles are drawn one after the other with replacement, what is the probability that both marbles are red?
   
   1. Calculate the probability of drawing a red marble first: $\frac{4}{10} = 0.4$.
   2. Since the marble is replaced, the probability remains the same for the second draw: $0.4$.
   3. Multiply the individual probabilities: $0.4 \times 0.4 = 0.16$.
   4. The probability is $\frac{16}{100}$ or $\frac{4}{25}$.
3. Example 3: Median of a Frequency Distribution
   A set of scores consists of three 10s, four 15s, and two 20s. What is the median score?
   
   1. List the data in ascending order: 10, 10, 10, 15, 15, 15, 15, 20, 20.
   2. Count the total number of items: $n = 9$.
   3. Identify the middle position: $\frac{9+1}{2} = 5$.
   4. The 5th value in the ordered list is 15.

Practice Questions

1. A set of 5 distinct integers has a mean of 12 and a median of 10. If the smallest integer is 4, what is the maximum possible value for the largest integer?

2. In a group of 100 students, 60 study Spanish, 45 study French, and 20 study both. How many students study neither Spanish nor French?

3. A pie chart shows the budget distribution of a city. If the "Education" sector accounts for $72^\circ$ of the circle and the total budget is $5,000,000, how much money is allocated to Education?

4. The standard deviation of Set A is 5.2. If every number in Set A is increased by 10, what is the new standard deviation?

5. A box contains 5 green balls and 3 yellow balls. If two balls are selected at random without replacement, what is the probability that both are yellow?

6. A bar graph indicates that sales in Q1 were $20,000 and sales in Q2 were $25,000. By what percent must Q2 sales increase to reach a target of $35,000 in Q3?

7. If the mean of $x, x+3,$ and $2x-1$ is 10, what is the value of $x$?

8. In a normal distribution, approximately what percentage of the data falls within two standard deviations of the mean?

Answers & Explanations

1. Answer: 23.
   The sum of the 5 integers is $5 \times 12 = 60$. Let the integers be $a, b, c, d, e$ in ascending order. We know $a=4$ and $c=10$. To maximize $e$, we must minimize $b$ and $d$. Since they are distinct integers, the smallest possible value for $b$ is 5. The smallest possible value for $d$ must be greater than the median (10), so $d=11$. Thus, $4 + 5 + 10 + 11 + e = 60$, which simplifies to $30 + e = 60$, so $e = 30$. Wait, if $d=11$, then $e = 30$. Let's recheck: $4, 5, 10, 11, 30$. The integers are distinct. Max value is 30. (Note: Ensure you read "distinct" carefully).
2. Answer: 15.
   Using the principle of inclusion-exclusion: Total = (Spanish) + (French) - (Both) + (Neither). $100 = 60 + 45 - 20 + N$. $100 = 85 + N$, so $N = 15$.
3. Answer: $1,000,000.
   A full circle is $360^\circ$. The fraction of the budget is $\frac{72}{360} = \frac{1}{5}$. Thus, $\frac{1}{5} \times 5,000,000 = 1,000,000$.
4. Answer: 5.2.
   Standard deviation measures the spread of data. Adding a constant to every value in a set shifts the mean but does not change the distances between the numbers. Therefore, the standard deviation remains unchanged.
5. Answer: $\frac{3}{28}$.
   The probability of the first ball being yellow is $\frac{3}{8}$. Since it is not replaced, there are 7 balls left, 2 of which are yellow. The probability of the second being yellow is $\frac{2}{7}$. Multiply: $\frac{3}{8} \times \frac{2}{7} = \frac{6}{56} = \frac{3}{28}$.
6. Answer: 40%.
   The increase needed is $35,000 - 25,000 = 10,000$. The percent increase is $\frac{10,000}{25,000} \times 100 = 0.4 \times 100 = 40\%$.
7. Answer: 7.
   The sum of the values is $x + x + 3 + 2x - 1 = 4x + 2$. Since the mean is 10, the sum is $3 \times 10 = 30$. Solve $4x + 2 = 30 \rightarrow 4x = 28 \rightarrow x = 7$.
8. Answer: 95%.
   According to the empirical rule for normal distributions (often cited in statistics resources), approximately 68% falls within 1 SD, 95% within 2 SDs, and 99.7% within 3 SDs.

1. If the range of a set of seven numbers is 0, which of the following must be true?

• AThe mean is 0
• BThe median is 0
• CAll numbers in the set are identical
• DThe mean is greater than the median

Frequently Asked Questions

What topics are covered in GRE Data Analysis?

The GRE Data Analysis section covers descriptive statistics (mean, median, mode, range, standard deviation), interpretation of graphs and tables, elementary probability, and counting methods like permutations and combinations. It tests your ability to extract meaning from data rather than performing complex calculus.

How should I handle Data Interpretation sets on the GRE?

Scan the titles, axes, and legends of the graphs before reading the questions to understand the context. Pay close attention to the units of measurement and look for trends or anomalies in the data that the questions might target. Using an AI Exam Simulator can help you get used to the time pressure of these specific sets.

Is standard deviation frequently tested on the GRE?

Yes, but the GRE usually tests the conceptual understanding of standard deviation rather than requiring you to calculate it manually. You should know how it changes when data is shifted or scaled and how it relates to the spread of a distribution. For more practice, you might look into quantitative biology questions which often use similar statistical concepts.

What is the difference between a permutation and a combination?

A permutation is used when the order of selection matters, such as assigning specific seats to people. A combination is used when the order does not matter, such as choosing a committee or a group of toppings for a pizza. To reinforce these concepts, try the Retrieval Challenge for daily math fact practice.

Can I use a calculator for Data Analysis questions?

Yes, an on-screen calculator is provided during the GRE Quantitative sections. It is useful for percent change calculations and finding means, but you should rely on logical estimation for many graph-based questions to save time. Integrating these habits into your AI MasterPlan will ensure consistent progress.