Hard GRE Data Analysis Set 1 Practice Questions

Concept Explanation

GRE data analysis is the subset of the Quantitative Reasoning section that evaluates your ability to interpret, model, and analyze data presented in tables, graphs, and probability distributions.

At a high difficulty level, these questions move beyond simple reading of values and require multi-step arithmetic, a deep understanding of standard deviation, and the ability to calculate conditional probabilities or complex weighted averages. Success in this area depends on identifying the specific statistical measures being tested—such as mean, median, mode, and range—and applying them to data sets that may include outliers or skewed distributions. You must also be proficient in interpreting cumulative frequency graphs and boxplots, which are frequent targets for Hard GRE Data Analysis Set 1 Practice Questions.

When tackling these problems, it is helpful to use an AI Exam Simulator to get accustomed to the digital interface and the specific ways the GRE presents visual data. Effective data analysis often involves "cleaning" the information mentally: ignoring irrelevant categories in a table and focusing strictly on the variables described in the question prompt.

Solved Examples

1. Example 1: Weighted Averages
   In a certain company, the average salary of the 20 technical employees is $65,000, and the average salary of the 30 administrative employees is $45,000. If the company hires 10 executives with an average salary of $120,000, what is the new average salary for all 60 employees?
   1. Calculate the total sum of salaries for each group: Technical = $20 \ \times 65,000 = 1,300,000$; Administrative = $30 \ \times 45,000 = 1,350,000$; Executives = $10 \ \times 120,000 = 1,200,000$.
   2. Find the grand total sum: $1,300,000 + 1,350,000 + 1,200,000 = 3,850,000$.
   3. Divide by the total number of employees: $\ \frac{3,850,000}{60} \approx 64,166.67$.
2. Example 2: Standard Deviation and Distribution
   Set A consists of the integers {10, 12, 14, 16, 18}. Set B consists of the integers {110, 112, 114, 116, 118}. Which set has a higher standard deviation?
   1. Recall the definition of standard deviation: it measures the spread of data points from the mean.
   2. Compare the distances between points in Set A: they are spaced 2 units apart.
   3. Compare the distances in Set B: they are also spaced 2 units apart.
   4. Since the relative spread is identical, the standard deviations are equal. Adding a constant to every value in a set does not change the standard deviation.
3. Example 3: Probability of Independent Events
   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. The probability of the first marble being red is $\ \frac{4}{10}$.
   2. Since there is no replacement, there are now 3 red marbles and 9 total marbles left.
   3. The probability of the second marble being red is $\ \frac{3}{9}$.
   4. Multiply the probabilities: $\ \frac{4}{10} \ \times \ \frac{3}{9} = \ \frac{12}{90} = \ \frac{2}{15}$.

Practice Questions

1. In a set of 150 measurements, the mean is 75 and the standard deviation is 8. If every measurement is increased by 10 and then multiplied by 2, what is the new standard deviation of the set?

2. A survey of 400 households found that 220 households own a dog, 160 own a cat, and 50 own both. How many households own neither a dog nor a cat?

3. The median of a list of 9 distinct integers is 42. If the three largest integers are increased by 15 each, what is the median of the new list?

4. A box contains 5 red balls, 4 green balls, and 3 white balls. If 3 balls are selected at random without replacement, what is the probability that at least one ball is white?

5. In a normal distribution, approximately what percent of the data falls within 2 standard deviations of the mean? You can refer to Khan Academy's guide on normal distributions for standard percentages.

6. The average (arithmetic mean) of 7 numbers is 12. If the average of 4 of these numbers is 8, what is the average of the remaining 3 numbers?

7. A data set consists of the following values: {x, 12, 15, 22, 22, 30}. If the range of the set is 25 and x is the smallest value, what is the mean of the set?

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

Answers & Explanations

1. 16: Adding a constant (10) to each value does not change the standard deviation. However, multiplying each value by a constant (2) multiplies the standard deviation by that same constant. $8 \ \times 2 = 16$.
2. 70: Use the formula for the union of two sets: $n(A ∪ B) = n(A) + n(B) - n(A ∩ B)$. So, $220 + 160 - 50 = 330$. The number of households with neither is $400 - 330 = 70$.
3. 42: The median is the middle value in an ordered list. Increasing the three largest values does not change the middle position or the value at that position, so the median remains 42. You can practice similar logic with GRE Practice Questions with Explanations.
4. 37/44: Use the complement: $1 - P(\ \text{no white balls})$. Total balls = 12. Prob(no white) = $\ \frac{9}{12} \ \times \ \frac{8}{11} \ \times \ \frac{7}{10} = \ \frac{3}{4} \ \times \ \frac{8}{11} \ \times \ \frac{7}{10} = \ \frac{168}{440} = \ \frac{21}{55}$. Thus, $1 - \ \frac{21}{55} = \ \frac{34}{55}$. (Correction: Calculation check: $\ \frac{3}{4} \ \times \ \frac{8}{11} \ \times \ \frac{7}{10} = \ \frac{504}{1320} = \ \frac{7}{11} \ \times \ \frac{3}{10} \dots$ simplified is $\ \frac{7}{22}$. $1 - \ \frac{7}{22} = \ \frac{15}{22}$ or $\ \frac{30}{44}$). Let's re-verify: $\ \frac{9 × 8 × 7}{12 × 11 × 10} = \ \frac{504}{1320} = \ \frac{21}{55}$. Result is $1 - 21/55 = 34/55$.
5. 95%: In a standard normal distribution, about 68% falls within 1 SD, 95% within 2 SDs, and 99.7% within 3 SDs.
6. 17.33: Sum of 7 numbers = $7 × 12 = 84$. Sum of 4 numbers = $4 × 8 = 32$. Sum of remaining 3 = $84 - 32 = 52$. Average = $52 / 3 = 17.33$.
7. 17.67: Range = Max - Min. $25 = 30 - x$, so $x = 5$. The set is {5, 12, 15, 22, 22, 30}. Sum = 106. Mean = $106 / 6 \approx 17.67$.
8. 0.3: $P(\ \text{not A}) = 0.6$ and $P(\ \text{not B}) = 0.5$. Since independent, multiply: $0.6 × 0.5 = 0.30$.

1. If the standard deviation of a data set is 0, what can be concluded about the data?

• AAll values are zero
• BThe mean is zero
• CAll values are identical
• DThe range is unknown

Frequently Asked Questions

How does the GRE test standard deviation?

The GRE rarely asks you to calculate the exact standard deviation using the formula. Instead, it tests your conceptual understanding of how data spread affects the value and how transformations like addition or multiplication change it.

What is the difference between mutually exclusive and independent events?

Mutually exclusive events cannot happen at the same time, while independent events are those where the occurrence of one does not affect the probability of the other. These are distinct statistical concepts that require different mathematical treatments.

How do I handle data interpretation sets with multiple graphs?

Always read the titles and axes of every graph first to understand the relationship between them. Often, one graph provides a total value while a second graph breaks that total down into percentages or categories.

What is a weighted average on the GRE?

A weighted average occurs when different groups in a set contribute different amounts to the overall mean based on their size. You must multiply each group's average by its count before summing and dividing by the total count.

Are outliers common in hard GRE data analysis questions?

Yes, outliers are frequently used to test whether a student knows that the median is more robust than the mean. Harder questions may ask how removing an outlier would shift the mean versus the median.