Easy GRE Statistical Analysis Questions Practice Questions

Concept Explanation

Statistical analysis on the GRE involves interpreting data sets using fundamental measures of central tendency, dispersion, and probability to evaluate numerical relationships. These concepts allow test-takers to summarize large amounts of information into single representative values like the mean, median, and mode. At the easy level, you will primarily encounter questions that ask you to calculate these averages or determine the range and standard deviation of a small list of numbers. Understanding how a single change in a data set affects these values is a core skill for the GRE Quantitative Reasoning section.

The arithmetic mean is calculated by summing all values in a set and dividing by the number of values. The median is the middle value when the data is ordered from least to greatest; if there is an even number of values, it is the average of the two middle terms. The mode is simply the value that appears most frequently. Beyond central tendency, you must understand measures of spread. The range is the difference between the greatest and least values, while standard deviation measures how spread out the numbers are from the mean. For a more comprehensive look at the exam structure, check out our GRE Prep hub.

Solved Examples

1. Finding the Median: A set of test scores consists of 85, 92, 78, 88, and 95. What is the median score?
   1. First, arrange the numbers in ascending order: 78, 85, 88, 92, 95.
   2. Identify the middle term in the list. Since there are 5 terms, the 3rd term is the middle.
   3. The median is 88.
2. Calculating the Mean with a Missing Value: The average of four numbers is 20. If three of the numbers are 15, 22, and 18, what is the fourth number?
   1. Use the sum formula: $\text{Sum} = \text{Average} \times \text{Number of items}$.
   2. Calculate the total sum: $20 \times 4 = 80$.
   3. Sum the known numbers: $15 + 22 + 18 = 55$.
   4. Subtract the known sum from the total sum: $80 - 55 = 25$.
   5. The fourth number is 25.
3. Range and Standard Deviation Concepts: Set A is {10, 10, 10, 10} and Set B is {5, 10, 15, 20}. Which set has a higher standard deviation?
   1. Standard deviation measures the distance of values from the mean.
   2. In Set A, every value is identical to the mean (10), so the standard deviation is 0.
   3. In Set B, the values vary significantly from the mean (12.5).
   4. Therefore, Set B has a higher standard deviation.

Practice Questions

1. A set of numbers consists of {4, 8, 12, 16, 20}. What is the arithmetic mean of this set?

2. In a sequence of 7 consecutive integers, the median is 12. What is the greatest integer in the sequence?

3. A shopper buys 5 items costing $12, $15, $12, $20, and $16. What is the mode of these prices?

4. If the range of a set of five distinct positive integers is 10 and the smallest integer is 3, what is the largest possible integer in the set?

5. The average of three numbers is 50. If two of the numbers are 45 and 55, what is the third number?

6. A data set contains the values {2, 4, 6, 8, 10, 12}. What is the median of this data set?

7. If the standard deviation of Set X is 0, what can be concluded about the elements in Set X?

8. Which of the following sets has the largest range: {1, 2, 3}, {10, 20, 30}, or {100, 101, 102}?

Answers & Explanations

1. Answer: 12. Sum the numbers: $4 + 8 + 12 + 16 + 20 = 60$. Divide by the count: $60 / 5 = 12$. For more drills, try our GRE Practice Questions with Answers.
2. Answer: 15. In a set of consecutive integers, the median is the middle term. If the 4th term is 12, the sequence is 9, 10, 11, 12, 13, 14, 15. The greatest is 15.
3. Answer: $12. The mode is the value that appears most often. In the list ($12, $15, $12, $20, $16), $12 appears twice, while others appear once.
4. Answer: 13. Range is defined as $\text{Greatest} - \text{Least}$. Given $10 = \text{Greatest} - 3$, solving for the greatest gives 13.
5. Answer: 50. The total sum must be $50 \times 3 = 150$. The sum of the first two is $45 + 55 = 100$. Thus, $150 - 100 = 50$.
6. Answer: 7. With an even number of terms (6), the median is the average of the 3rd and 4th terms: $\frac{6 + 8}{2} = 7$.
7. Answer: All elements are identical. Standard deviation measures variation from the mean. If there is zero variation, every number in the set must be the same. This is a common concept in AI-powered GRE practice questions.
8. Answer: {10, 20, 30}. The ranges are: $3-1=2$, $30-10=20$, and $102-100=2$. The second set has the largest range.

1. What happens to the mean of a set if every number in the set is increased by 5?

• AThe mean stays the same
• BThe mean increases by 5
• CThe mean increases by 25
• DThe mean decreases by 5

Frequently Asked Questions

What is the difference between mean and median on the GRE?

The mean is the average of all numbers, while the median is the specific middle value of an ordered list. The mean is sensitive to outliers, whereas the median provides a better sense of the "center" when extreme values are present.

How do I calculate the weighted average?

To find a weighted average, multiply each value by its corresponding weight (or frequency), sum those products, and then divide by the total sum of the weights. This is common when different groups in a problem have different sizes.

Can the standard deviation ever be negative?

No, standard deviation can never be negative because it is calculated using the square root of squared differences. The smallest possible value for standard deviation is zero, which occurs when all numbers in a set are identical.

Does the GRE provide a calculator for statistics?

Yes, the GRE provides an on-screen calculator for the Quantitative Reasoning section. You can use it to sum large lists of numbers or perform division for mean calculations, though many easy questions can be solved with mental math. For more tools, visit our AI Question Generator.

What is the relationship between the range and standard deviation?

Both are measures of dispersion, but the range only considers the two extreme values of a set. Standard deviation is a more sophisticated measure that considers how every single value in the set relates to the mean.