Hard GRE Data Analysis Exam Questions Practice Questions

Concept Explanation

GRE Data Analysis involves the interpretation, analysis, and manipulation of data presented in tables, graphs, and statistical distributions. These questions test your ability to apply descriptive statistics, probability, and counting methods to complex, real-world scenarios. To succeed on Hard GRE Data Analysis Exam Questions, you must move beyond simple arithmetic and understand the nuances of standard deviation, normal distributions, and weighted averages. The GRE often requires you to synthesize information from multiple charts or identify subtle trends that are not immediately obvious. Understanding the mathematical properties of normal distributions and the logic of combinations and permutations is essential for high-level performance.

Data interpretation is a significant component of the GRE Prep curriculum. On the harder end of the spectrum, the exam will challenge your precision. You might encounter a data set where you have to calculate the percentage change between two values that are themselves derived from other percentages. Success requires a methodical approach: identify the specific data point requested, determine the operations needed, and be wary of unit conversions or trap answers based on common misconceptions. Students often find that using tools like an AI Question Generator helps them practice the specific logic required for these multi-step problems.

Solved Examples

1. Problem: In a set of 10 numbers, the mean is 50 and the standard deviation is 0. If every number in the set is increased by 5, what is the new mean and the new standard deviation?
   1. Identify the properties of standard deviation. Standard deviation measures spread. If all numbers are the same (SD = 0), then every number in the set is 50.
   2. Apply the change. If every number increases by 5, every number becomes 55.
   3. Calculate the new mean. Since all numbers are 55, the new mean is $\frac{55 \times 10}{10} = 55$.
   4. Calculate the new standard deviation. Since all numbers are still identical (all are 55), there is no spread. Thus, the new SD is still 0.
2. Problem: A bag contains 4 red marbles and 6 blue marbles. If 3 marbles are drawn at random without replacement, what is the probability that exactly 2 are red?
   1. Calculate the total number of ways to choose 3 marbles from 10: $$\binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120$$
   2. Calculate the number of ways to choose exactly 2 red marbles from 4: $$\binom{4}{2} = \frac{4 \times 3}{2 \times 1} = 6$$
   3. Calculate the number of ways to choose the remaining 1 marble from the 6 blue marbles: $$\binom{6}{1} = 6$$
   4. Multiply the favorable outcomes: $6 \times 6 = 36$.
   5. Divide by total outcomes: $\frac{36}{120} = \frac{3}{10}$ or 0.3.
3. Problem: If the ratio of the number of men to women in a room is 3:4 and the average age of the men is 32 while the average age of the women is 25, what is the average age of everyone in the room?
   1. Use the weighted average formula. Let the number of men be $3x$ and the number of women be $4x$.
   2. Calculate the total sum of ages: $(3x \times 32) + (4x \times 25) = 96x + 100x = 196x$.
   3. Divide the total sum by the total number of people ($3x + 4x = 7x$): $$\text{Average} = \frac{196x}{7x} = 28$$

Practice Questions

1. A distribution of test scores has a mean of 72 and a standard deviation of 8. If the scores are normally distributed, approximately what percent of the scores are greater than 88?

2. Set A consists of the integers {2, 4, 6, 8, 10}. Set B consists of the integers {2, 4, 6, 8, 10, 12}. Which set has a higher standard deviation, and by how much (rounded to one decimal)?

3. A committee of 4 people is to be chosen from a group of 5 men and 5 women. What is the probability that the committee will have an equal number of men and women?

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

5. The average (arithmetic mean) of 7 consecutive integers is 15. What is the average of the first 4 of these integers?

6. A certain stock's price increased by 20% in January and then decreased by 10% in February. What was the net percentage change in the stock price over the two months?

7. Box X contains 3 red balls and 2 green balls. Box Y contains 2 red balls and 4 green balls. If one ball is drawn at random from each box, what is the probability that both balls are the same color?

8. Seven people are to be seated in a row of seven chairs. If two of the people, Alice and Bob, must sit next to each other, how many different seating arrangements are possible?

9. A set of data consists of 5 positive integers. The median is 12, the mode is 8, and the range is 10. What is the largest possible value for the mean of this set?

10. If the probability of an event occurring is $p$, and the probability of it not occurring is $q$, what is the value of $p^2 + 2pq + q^2$?

Answers & Explanations

1. 2.5%: In a normal distribution, 95% of data falls within 2 standard deviations of the mean. A score of 88 is exactly 2 standard deviations above the mean ($72 + 2 \times 8 = 88$). The remaining 5% is split between the two tails; thus, 2.5% is above 88.
2. Set B; 0.6: The standard deviation of Set A is approximately 2.8. Adding 12 to the set increases the spread from the mean, resulting in a standard deviation of approximately 3.4 for Set B.
3. 10/21: Total ways to choose 4 from 10 is $\binom{10}{4} = 210$. Ways to choose 2 men and 2 women: $\binom{5}{2} \times \binom{5}{2} = 10 \times 10 = 100$. Probability = $\frac{100}{210} = \frac{10}{21}$.
4. 15: Using the formula $n(A \cup B) = n(A) + n(B) - n(A \cap B)$, we get $60 + 45 - 20 = 85$. Students studying neither = $100 - 85 = 15$.
5. 13.5: If the average of 7 consecutive integers is 15, the integers are 12, 13, 14, 15, 16, 17, 18. The first four are 12, 13, 14, 15. Their average is $\frac{12+13+14+15}{4} = 13.5$.
6. 8%: Let the initial price be 100. After Jan: $100 \times 1.2 = 120$. After Feb: $120 \times 0.9 = 108$. The change from 100 to 108 is an 8% increase.
7. 7/15: P(Both Red) = $\frac{3}{5} \times \frac{2}{6} = \frac{6}{30}$. P(Both Green) = $\frac{2}{5} \times \frac{4}{6} = \frac{8}{30}$. Total = $\frac{14}{30} = \frac{7}{15}$.
8. 1,440: Treat Alice and Bob as one unit. There are now 6 units to arrange (6!). Within the unit, Alice and Bob can swap (2!). Total = $720 \times 2 = 1440$.
9. 13.2: The set must have two 8s (mode). The median is 12. To maximize the mean, maximize the other numbers. Set: {8, 8, 12, x, y}. Range is 10, so $y - 8 = 10$, meaning $y = 18$. To maximize x, it must be less than or equal to y, but x is the 4th value. Max x is 18. Set: {8, 8, 12, 18, 18}. Mean = $\frac{64}{5} = 12.8$. (Correction: If integers must be distinct except for mode, x=17, but GRE usually allows non-distinct. Using {8,8,12,18,18} gives 12.8).
10. 1: Since $p + q = 1$ (the sum of the probability of an event and its complement), the expression $p^2 + 2pq + q^2$ is the expansion of $(p+q)^2$. Thus, $1^2 = 1$.

1. If the standard deviation of a data set is 5, what is the variance?

• A2.5
• B10
• C25
• D50

Frequently Asked Questions

How is standard deviation tested on the GRE?

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

What is the difference between a combination and a permutation?

A permutation is used when the order of selection matters, such as seating people in specific chairs. A combination is used when the order does not matter, such as choosing a group of people for a committee.

How do I handle "Select All That Apply" data questions?

Treat each option as a separate True/False question. These are common in GRE Reading Exam Questions and Data Analysis, requiring you to verify every statement against the provided charts before moving on.

What is a normal distribution on the GRE?

A normal distribution is a bell-shaped curve where the mean, median, and mode are equal. You should memorize the 68-95-99.7 rule, which describes the percentage of data within one, two, and three standard deviations from the mean.

Can I use a calculator for Data Analysis questions?

Yes, the GRE provides an on-screen calculator. However, for Hard GRE Data Analysis Exam Questions, the calculator is often less helpful than logical reasoning and understanding properties of numbers.