Easy GRE Statistics Practice Questions Practice Questions

Statistics represent a fundamental portion of the GRE Quantitative Reasoning section, testing your ability to interpret, analyze, and manipulate data sets. These concepts are not just academic exercises; according to the Educational Testing Service (ETS), data analysis accounts for approximately 25% of the math content on the exam. Understanding how to calculate the arithmetic mean, identify the median, and determine the range is essential for any student aiming for a high score. By focusing on Easy GRE Statistics Practice Questions, you can build a solid foundation before moving on to complex standard deviation or normal distribution problems.

Concept Explanation

GRE statistics is the study of data sets through measures of central tendency (mean, median, mode) and measures of dispersion (range, interquartile range, standard deviation). These tools allow you to summarize large amounts of information into single, representative values. The arithmetic mean is the average of a set, calculated by dividing the sum of all terms by the number of terms. The median is the middle value when the data is ordered from least to greatest. If there is an even number of terms, the median is the average of the two middle terms. The mode is the value that appears most frequently. Dispersion measures, like the range, tell us how spread out the data is by subtracting the minimum value from the maximum value. You can find more comprehensive resources on our GRE Prep hub.

Term	Definition	Formula/Method
Arithmetic Mean	The average of the set.	$\frac{ \text{Sum of values}}{ \text{Number of values}}$
Median	The middle value.	Order set; find center.
Range	The spread of the data.	$\text{Max} - \text{Min}$

Solved Examples

1. Finding the Mean: A student takes four exams and scores 82, 88, 90, and 92. What is the average score?
   1. Sum the scores: $82 + 88 + 90 + 92 = 352$.
   2. Count the number of items: there are 4 exams.
   3. Divide the sum by the count: $\frac{352}{4} = 88$.
   4. The average score is 88.
2. Determining the Median: Find the median of the set: $\{15, 7, 22, 13, 10\}$.
   1. Arrange the numbers in ascending order: $\{7, 10, 13, 15, 22\}$.
   2. Identify the middle term. Since there are 5 terms, the 3rd term is the middle.
   3. The median is 13.
3. Calculating the Range: In a local weather report, the daily high temperatures for a week were $65^\circ, 72^\circ, 68^\circ, 80^\circ, 75^\circ, 71^\circ, \text{ and } 69^\circ$. What is the range?
   1. Identify the maximum value: $80$.
   2. Identify the minimum value: $65$.
   3. Subtract the minimum from the maximum: $80 - 65 = 15$.
   4. The range is 15.

Practice Questions

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

2. If the median of the set $\{x, 10, 15, 20, 25\}$ is 15, and the numbers are listed in increasing order, what is the smallest possible integer value for $x$?

3. A basketball player scores 12, 18, 15, 22, and 13 points in five games. What is the range of the points scored?

4. In a set of six integers $\{2, 4, 4, 7, 9, 10\}$, which value represents the mode?

5. If the sum of five numbers is 100, what is the arithmetic mean of these numbers?

6. Find the median of the following set of even numbers: $\{2, 4, 6, 8, 10, 12\}$.

7. A set of data is $\{5, 5, 5, 5, 5\}$. What is the standard deviation of this set?

8. If the mean of three numbers is 10, and two of the numbers are 7 and 11, what is the third number?

9. A list of numbers has a range of 20. If the smallest number is -5, what is the largest number?

10. Quantity A: The mean of $\{10, 20, 30\}$. Quantity B: The median of $\{10, 20, 30\}$. Compare the two quantities.

Answers & Explanations

1. Answer: 12. Sum the values: $4 + 8 + 12 + 16 + 20 = 60$. Divide by the count: $60 / 5 = 12$.
2. Answer: Any integer less than or equal to 10. Since the set is in increasing order, $x$ must be the smallest value. As long as $x \leq 10$, 15 remains the middle term.
3. Answer: 10. The maximum is 22 and the minimum is 12. Range = $22 - 12 = 10$.
4. Answer: 4. The mode is the most frequent number. Here, 4 appears twice, while all other numbers appear once.
5. Answer: 20. Mean = $\text{Sum} / \text{Count}$. Mean = $100 / 5 = 20$. For more practice on basic math, check out GRE Practice Questions with Answers.
6. Answer: 7. With an even number of terms (6), the median is the average of the 3rd and 4th terms: $(6 + 8) / 2 = 7$.
7. Answer: 0. Standard deviation measures spread. Since all numbers are identical, there is no spread, so the deviation is zero.
8. Answer: 12. Let the third number be $x$. $(7 + 11 + x) / 3 = 10$. Multiplying gives $18 + x = 30$, so $x = 12$.
9. Answer: 15. Range = Max - Min. $20 = \text{Max} - (-5)$. $20 = \text{Max} + 5$, so Max = 15.
10. Answer: They are equal. Mean = $(10+20+30)/3 = 20$. Median = 20. Both quantities are 20.

1. If a data set is {3, 3, 3, 3, 3}, what is the range?

• A3
• B0
• C1
• D5

Frequently Asked Questions

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

The mean is the calculated average of all numbers in a set, whereas the median is the physical middle value when the numbers are ordered. The mean is sensitive to outliers, while the median remains stable even if the highest or lowest values change drastically.

How do I find the median if the set has an even number of terms?

When a set contains an even number of values, there is no single middle number. To find the median, you must take the arithmetic mean of the two middle-most numbers after sorting the set in ascending order.

Can the range of a data set be negative?

No, the range can never be negative because it is calculated by subtracting the smaller value from the larger value. If all numbers in the set are the same, the range is zero; otherwise, it is always a positive value.

What does a standard deviation of zero mean?

A standard deviation of zero indicates that there is no variation in the data set. This specifically means that every single value in the set is identical to the mean, resulting in no spread or dispersion.

Is the mode always a single number?

A data set can have one mode, more than one mode (bimodal or multimodal), or no mode at all if no number repeats. On the GRE, you may encounter sets where multiple numbers share the highest frequency.