GRE Data Analysis Set 2 Practice Questions with Answers

Data interpretation and statistical reasoning account for approximately 25% of the quantitative reasoning score on the Graduate Record Examination. This GRE Data Analysis Set 2 Practice Questions with Answers guide provides the rigorous preparation needed to navigate complex charts, probability scenarios, and frequency distributions. By engaging with these specific problems, you can refine your ability to extract meaningful insights from raw information, a skill highly valued by Educational Testing Service (ETS) evaluators. Success in this section requires more than basic arithmetic; it demands a strategic approach to visual data and a deep understanding of measures of central tendency.

Concept Explanation

GRE Data Analysis involves the interpretation of data presented in tables, graphs, and charts, alongside the application of basic statistics, probability, and counting methods. This domain tests your capacity to identify trends, calculate percentages of change, and understand the properties of normal distributions. To excel, you must be comfortable with GRE Prep strategies that focus on reading axes correctly and recognizing when data is insufficient to answer a specific question. Key sub-topics include descriptive statistics (mean, median, mode, range, and standard deviation), elementary probability, and data representation through bar graphs, circle graphs, and boxplots.

Solved Examples

1. Problem: A set of five integers has a mean of 12 and a median of 10. If the smallest integer is 5 and the largest is 20, what is the sum of the remaining two integers?
   1. Identify the total sum: Since the mean of 5 integers is 12, the total sum is $5 \times 12 = 60$.
   2. Subtract known values: The sum of the smallest and largest integers is $5 + 20 = 25$. The remaining sum for the three middle integers is $60 - 25 = 35$.
   3. Use the median: The median is the middle value when ordered. So, the set looks like $\{5, x, 10, y, 20\}$.
   4. Solve for the unknown pair: The sum of the two unknown integers $x$ and $y$ is found by subtracting the median from the remaining sum: $35 - 10 = 25$.
   5. Answer: The sum of the remaining two integers is 25.
2. Problem: In a group of 80 students, 45 study French, 30 study Spanish, and 10 study both. How many students study neither language?
   1. Apply the Principle of Inclusion-Exclusion: Total students studying at least one language = $\text{French} + \text{Spanish} - \text{Both}$.
   2. Calculate: $45 + 30 - 10 = 65$.
   3. Subtract from the total population: $80 - 65 = 15$.
   4. Answer: 15 students study neither language.
3. Problem: A bag contains 4 red marbles and 6 blue marbles. If two marbles are drawn at random without replacement, what is the probability that both are red?
   1. Find the probability of the first draw: $P( \text{Red}_1) = \frac{4}{10} = \frac{2}{5}$.
   2. Find the probability of the second draw given the first was red: $P( \text{Red}_2 | \text{Red}_1) = \frac{3}{9} = \frac{1}{3}$.
   3. Multiply the probabilities: $\frac{2}{5} \times \frac{1}{3} = \frac{2}{15}$.
   4. Answer: The probability is $\frac{2}{15}$.

Practice Questions

1. A company’s revenue increased from $4.5 million in 2020 to $5.4 million in 2021. What was the percent increase in revenue?

2. If the standard deviation of a set of numbers $\{x, y, z\}$ is $s$, what is the standard deviation of the set $\{x+5, y+5, z+5\}$?

3. A boxplot shows a distribution where the first quartile is 15, the median is 22, and the third quartile is 30. What is the interquartile range (IQR)?

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

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

6. The average (arithmetic mean) of 7 numbers is 12. If one number is removed, the average of the remaining 6 numbers becomes 13. What number was removed?

7. A pie chart representing a budget shows that "Rent" accounts for 35% of the total. If the total budget is $4,000, what is the central angle of the "Rent" sector in degrees?

8. A set of data consists of the values: 4, 8, 8, 12, 15, 15, 15, 20. What is the mode of this data set?

9. If two fair six-sided dice are rolled, what is the probability that the sum of the numbers shown is 7?

10. If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.5, and A and B are independent, what is the probability that neither event A nor event B occurs?

Answers & Explanations

1. 20%: The percent increase is calculated as $\frac{ \text{New} - \text{Old}}{ \text{Old}} \times 100$. Here, $\frac{5.4 - 4.5}{4.5} = \frac{0.9}{4.5} = 0.2$, which is 20%.
2. $s$: Adding a constant to every value in a data set shifts the mean but does not change the spread or dispersion. Therefore, the standard deviation remains the same.
3. 15: The IQR is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$). $30 - 15 = 15$.
4. 95%: According to the empirical rule for normal distributions, approximately 68% falls within 1 SD, 95% within 2 SDs, and 99.7% within 3 SDs. You can learn more about these distributions on Wikipedia.
5. 35: Use the combinations formula $nCr = \frac{n!}{r!(n-r)!}$. Here, $7C3 = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$.
6. 6: Total sum of 7 numbers = $7 \times 12 = 84$. Total sum of 6 numbers = $6 \times 13 = 78$. The removed number is $84 - 78 = 6$.
7. $126^\circ$: A full circle is $360^\circ$. The angle for 35% is $0.35 \times 360 = 126^\circ$.
8. 15: The mode is the value that appears most frequently. 15 appears three times, while 8 appears twice and others appear once.
9. $\frac{1}{6}$: There are $6 \times 6 = 36$ total outcomes. The pairs that sum to 7 are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are 6 such pairs. $\frac{6}{36} = \frac{1}{6}$.
10. 0.3: The probability of A not occurring is $1 - 0.4 = 0.6$. The probability of B not occurring is $1 - 0.5 = 0.5$. Since they are independent, multiply them: $0.6 \times 0.5 = 0.3$.

1. If a data set has a range of 25 and every number in the set is multiplied by 2, what is the new range?

• A25
• B50
• C12.5
• DCannot be determined

Frequently Asked Questions

How does the GRE test data analysis differently than general math?

The GRE focuses on your ability to synthesize information from visual displays and apply statistical logic rather than just performing complex calculations. It requires a higher level of critical thinking regarding data validity and trend extrapolation compared to standard algebra or geometry sections.

What is the difference between a combination and a permutation on the GRE?

Combinations are used when the order of selection does not matter, such as picking a committee, whereas permutations are used when order is critical, such as arranging books on a shelf. You can practice these distinctions using the AI Question Generator to ensure you apply the correct formula during the exam.

Are calculators allowed during the GRE Data Analysis section?

Yes, an on-screen calculator is provided for the Quantitative Reasoning section, which includes Data Analysis. However, it is designed for basic operations, so you should rely on conceptual understanding to avoid time-consuming manual entry.

What is a "weighted average" and when should I use it?

A weighted average is used when different groups in a data set contribute differently to the final total, such as groups of different sizes. You calculate it by multiplying each value by its corresponding weight (or frequency) and dividing by the total weight.

How can I identify outliers in a GRE data set?

Outliers are values that fall significantly outside the overall pattern of the distribution, often defined as being more than 1.5 times the IQR above the third quartile or below the first quartile. On the GRE, they are often visually apparent in scatterplots or described as extreme values that skew the mean.