GRE Data Analysis Questions Practice Questions with Answers

Concept Explanation

GRE Data Analysis questions evaluate your ability to interpret, analyze, and draw conclusions from data presented in tables, graphs, and other visual formats. These questions primarily focus on descriptive statistics, such as mean, median, mode, and range, as well as probability, counting methods (combinations and permutations), and data interpretation. According to descriptive statistics fundamentals, the goal is to summarize a sample rather than use the data to learn about the population that the sample of data is thought to represent.

On the GRE, you will encounter various formats, including multiple-choice, multiple-choice with more than one correct answer, and numeric entry. To succeed, you must be comfortable with GRE Prep strategies that emphasize reading axes carefully and understanding the difference between absolute values and percentages. For example, a graph might show a 50% increase in sales, but if the original value was only $10, the actual growth is modest compared to a 5% increase on $1,000,000.

Key topics include:

• Measures of Central Tendency: Mean (average), Median (middle value), and Mode (most frequent).
• Measures of Dispersion: Range (difference between max and min) and Standard Deviation (how spread out numbers are from the mean).
• Probability: The likelihood of an event occurring, ranging from 0 to 1.
• Counting Methods: Using $n!$ (factorials), $\frac{n!}{(n-k)!}$ (permutations), and $\frac{n!}{k!(n-k)!}$ (combinations).
• Data Interpretation: Extracting specific values from bar charts, line graphs, circle graphs, and boxplots.

Solved Examples

1. In a set of five integers $\{x, 12, 15, 20, 25\}$, the mean is 18. What is the value of $x$?

1. Recall the formula for the mean: $\text{Mean} = \frac{ \text{Sum of values}}{ \text{Number of values}}$.
2. Set up the equation: $18 = \frac{x + 12 + 15 + 20 + 25}{5}$.
3. Multiply both sides by 5: $90 = x + 72$.
4. Subtract 72 from 90 to find $x = 18$.

2. A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. If two marbles are drawn at random without replacement, what is the probability that both are red?

1. Calculate the total number of marbles: $4 + 3 + 5 = 12$.
2. The probability that the first marble is red is $\frac{4}{12} = \frac{1}{3}$.
3. Since there is no replacement, the remaining marbles total 11, and the remaining red marbles total 3.
4. The probability that the second marble is red is $\frac{3}{11}$.
5. Multiply the probabilities: $\frac{1}{3} \times \frac{3}{11} = \frac{1}{11}$.

3. A company has 10 employees. In how many ways can a committee of 3 be chosen?

1. Determine if order matters. Since this is a committee where roles aren't specified, order does not matter; use the combination formula: $\binom{n}{k} = \frac{n!}{k!(n-k)!}$.
2. Plug in the values: $\binom{10}{3} = \frac{10!}{3!(10-3)!}$.
3. Simplify: $\frac{10 \times 9 \times 8}{3 \times 2 \times 1}$.
4. Calculate: $\frac{720}{6} = 120$.

Practice Questions

1. The heights of 6 students in centimeters are 150, 162, 150, 175, 180, and 155. What is the median height?

2. In a group of 40 people, 25 speak English, 15 speak French, and 10 speak both. How many people speak neither language?

3. If the standard deviation of a set of numbers $\{a, b, c, d\}$ is $s$, what is the standard deviation of the set $\{a+5, b+5, c+5, d+5\}$?

4. A boxplot displays data where the first quartile (Q1) is 20, the median is 35, and the third quartile (Q3) is 50. What is the Interquartile Range (IQR)?

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

6. If a set of data is normally distributed with a mean of 100 and a standard deviation of 10, approximately what percentage of the data falls between 80 and 120?

7. A restaurant offers 4 appetizers, 10 main courses, and 3 desserts. How many different 3-course meals (one from each category) are possible?

8. The average (arithmetic mean) of 7 numbers is 12. If one number is removed, the average of the remaining numbers becomes 11. What was the number removed?

9. A circle graph shows that 40% of a company's budget is spent on salaries. If the total budget is $1.2 million, how much is spent on expenses other than salaries?

10. How many different 4-letter "words" (arrangements) can be formed using the letters in the word "MATH" if each letter is used exactly once?

Answers & Explanations

1. 158.5 cm: First, arrange the heights in ascending order: 150, 150, 155, 162, 175, 180. Since there is an even number of values (6), the median is the average of the two middle values: $\frac{155 + 162}{2} = 158.5$.
2. 10: Use the formula for the union of two sets: $\text{Total} = n(E) + n(F) - n(E \cap F) + n( \text{Neither})$. So, $40 = 25 + 15 - 10 + n( \text{Neither})$. This simplifies to $40 = 30 + n( \text{Neither})$, meaning 10 people speak neither.
3. s: Adding a constant to every term in a data set shifts the mean but does not change the spread or distance between the numbers. Therefore, the standard deviation remains unchanged.
4. 30: The Interquartile Range is calculated as $Q3 - Q1$. Here, $50 - 20 = 30$.
5. 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 outcomes. Probability = $\frac{4}{36} = \frac{1}{9}$.
6. 95%: In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. Since 80 is $100 - 2(10)$ and 120 is $100 + 2(10)$, the range covers 95%.
7. 120: According to the fundamental counting principle, multiply the number of choices for each category: $4 \times 10 \times 3 = 120$.
8. 18: The total sum of the 7 numbers is $7 \times 12 = 84$. The total sum of the 6 numbers is $6 \times 11 = 66$. The removed number is $84 - 66 = 18$.
9. $720,000: If 40% is spent on salaries, 60% is spent on other expenses. $0.60 \times 1,200,000 = 720,000$.
10. 24: This is a permutation of 4 distinct items: $4! = 4 \times 3 \times 2 \times 1 = 24$.

1. If the range of a set of 10 numbers is 0, which of the following must be true?

• AThe mean is 0
• BThe median is 0
• CAll the numbers in the set are identical
• DThe standard deviation is 1

Frequently Asked Questions

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

A permutation is used when the order of selection matters, such as assigning specific roles or arranging letters, while a combination is used when the order does not matter, such as picking a group or committee. You can practice these distinctions using an AI Question Generator to see various scenarios.

How is standard deviation tested in GRE Data Analysis questions?

The GRE rarely asks you to calculate standard deviation manually; instead, it tests your understanding of how data spread affects the value and how adding or multiplying constants changes it. You should know that a higher standard deviation indicates that data points are further from the mean.

What are the most common graph types on the GRE?

The GRE frequently uses bar graphs, line graphs, circle graphs (pie charts), and scatterplots to present data. Occasionally, you may see more complex visuals like boxplots or frequency distributions that require identifying quartiles or peaks.

Can I use a calculator for Data Analysis questions?

Yes, the GRE provides an on-screen calculator, which is particularly helpful for Data Analysis questions involving large sums or multi-step percentage changes. However, it is often faster to use estimation or simplify fractions before resorting to the calculator.

What is the best way to improve at Data Interpretation?

The best method is to practice scanning graphs for labels, units, and axes before reading the questions to ensure you don't misinterpret the data scale. Using an AI Exam Simulator can help you get used to the time pressure and variety of data formats found on the actual test.