GRE Data Analysis Set 1 Practice Questions with Answers

Data analysis requires interpreting information from tables, charts, and graphs to draw logical conclusions about numerical relationships. Preparing for the quantitative reasoning section involves more than just arithmetic; it demands a critical eye for detail and the ability to synthesize data points into meaningful trends. By practicing with a GRE Data Analysis Set 1, students can familiarize themselves with the specific formatting and logic traps frequently employed by the Educational Testing Service (ETS). This foundation is essential for anyone aiming for a high score on the GRE Prep journey.

Concept Explanation

Data analysis on the GRE is the process of summarizing, organizing, and interpreting data presented in various visual or tabular formats to solve quantitative problems. This core concept encompasses descriptive statistics, basic probability, and data interpretation. You will encounter frequency distributions, measures of central tendency (mean, median, mode), and measures of dispersion like range and standard deviation. Furthermore, understanding normal distributions and the properties of the bell curve is vital for answering questions about percentiles and data spread. Calculations often involve percentages, ratios, and rates derived directly from the provided visuals. A common pitfall is misreading the units on an axis or failing to notice that a table represents change rather than absolute totals. Success in this area relies on a two-step approach: first, accurately extracting the necessary numbers from the graphic, and second, applying the correct mathematical formula to those numbers. Using tools like an AI Exam Simulator can help you get used to the time pressure associated with these multi-step problems.

Solved Examples

1. Example 1: Mean and Median
   A set of five integers is {12, 15, 18, 22, x}. If the mean of the set is 18, what is the value of x?
   
   1. Use the mean formula: $\text{Mean} = \frac{ \text{Sum of terms}}{ \text{Number of terms}}$.
   2. Set up the equation: $18 = \frac{12 + 15 + 18 + 22 + x}{5}$.
   3. Multiply both sides by 5: $90 = 67 + x$.
   4. Solve for x: $x = 23$.
2. Example 2: Interpreting a Bar Chart
   A bar chart shows that Company A made $4 million in 2020 and $5.2 million in 2021. What was the percent increase in revenue?
   
   1. Identify the change: $\$5.2 - \$4.0 = \$1.2$ million.
   2. Use the percent change formula: $\frac{ \text{Change}}{ \text{Original}} \times 100$.
   3. Calculate: $\frac{1.2}{4.0} = 0.3$.
   4. Convert to percentage: $0.3 \times 100 = 30\%$.
3. Example 3: Probability
   A bag contains 4 red marbles, 6 blue marbles, and 10 green marbles. If one marble is picked at random, what is the probability it is NOT blue?
   
   1. Find the total number of marbles: $4 + 6 + 10 = 20$.
   2. Find the number of marbles that are not blue: $4 \text{ (red)} + 10 \text{ (green)} = 14$.
   3. Form the probability fraction: $\frac{14}{20}$.
   4. Simplify the fraction: $\frac{7}{10}$ or 0.7.

Practice Questions

1. In a group of 10 students, the scores on a test were: 72, 85, 90, 65, 78, 90, 82, 88, 70, and 90. What is the mode of this data set?

2. A pie chart representing a household budget shows that 25% is spent on rent, 15% on food, and 10% on utilities. If the total monthly budget is $3,000, how much money is spent on food and utilities combined?

3. The standard deviation of a set of numbers {a, b, c, d} is s. If every number in the set is increased by 5, what is the new standard deviation?

4. A boxplot shows the distribution of heights in a class. The first quartile (Q1) is 62 inches and the third quartile (Q3) is 70 inches. What is the interquartile range (IQR)?

5. If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.5, and events A and B are independent, what is the probability that both A and B occur?

6. A table shows that the population of a city grew from 100,000 to 125,000 over 5 years. What was the average annual growth in population (simple average)?

7. In a normal distribution, approximately what percentage of the data falls within one standard deviation of the mean?

8. A set of numbers has a mean of 50. If a new number, 100, is added to the set, what happens to the mean?

Answers & Explanations

1. 90: The mode is the value that appears most frequently. In the set {72, 85, 90, 65, 78, 90, 82, 88, 70, 90}, the number 90 appears three times, which is more than any other number.
2. $750: First, add the percentages for food (15%) and utilities (10%) to get 25%. Then, calculate 25% of the total budget: $0.25 \times \$3,000 = \$750$.
3. s: Adding a constant to every term in a data set shifts the entire distribution but does not change the spread. Therefore, the standard deviation remains the same.
4. 8 inches: The interquartile range is calculated by subtracting Q1 from Q3: $70 - 62 = 8$.
5. 0.2: For independent events, the probability of both occurring is the product of their individual probabilities: $0.4 \times 0.5 = 0.2$.
6. 5,000: Total growth is $125,000 - 100,000 = 25,000$. Divide the total growth by the number of years: $\frac{25,000}{5} = 5,000$.
7. 68%: According to the empirical rule for a normal distribution, approximately 68% of data points fall within one standard deviation of the mean.
8. The mean increases: Since the new number (100) is greater than the current mean (50), adding it will pull the average upward.

1. If the range of a set of data is 20 and the smallest value is 5, what is the largest value?

• A15
• B20
• C25
• D30

Frequently Asked Questions

What topics are covered in GRE Data Analysis?

GRE Data Analysis covers basic statistics (mean, median, mode, range, standard deviation), probability, and the interpretation of graphs such as bar charts, line graphs, and scatter plots. It also includes concepts like permutations, combinations, and Venn diagrams.

How is the median calculated for an even number of data points?

If a data set has an even number of values, the median is the arithmetic mean of the two middle values after the set has been ordered. For example, in the set {2, 4, 6, 8}, the median is $\frac{4+6}{2} = 5$.

Does the GRE provide a calculator for data analysis questions?

Yes, the GRE provides an on-screen calculator for the quantitative section, which includes basic operations and a square root function. However, you should use it sparingly to save time on simple arithmetic.

What is the difference between a histogram and a bar chart?

A bar chart represents categorical data with spaces between bars, while a histogram represents continuous numerical data grouped into intervals (bins) with no spaces between the bars. Histograms are used to show the distribution of a single variable.

How should I handle questions with multiple graphs?

When faced with multiple graphs, first identify which graph contains the specific data requested by the question. Often, one graph provides a total value while the other provides a percentage breakdown, requiring you to combine information from both to find the answer.