GRE Statistics Practice Test Practice Questions with Answers

Twenty-five percent of the GRE Quantitative Reasoning section often focuses on data analysis, including topics like probability and descriptive statistics. Scoring high on these sections requires more than just memorizing formulas; you must understand how to interpret data sets and identify trends under timed conditions. Using a GRE Statistics Practice Test helps bridge the gap between theoretical knowledge and the fast-paced reality of the actual exam. By engaging with realistic scenarios, you can refine your ability to calculate measures of central tendency, dispersion, and normal distributions efficiently.

Concept Explanation

GRE statistics encompasses the study of data collection, analysis, interpretation, and presentation, focusing primarily on descriptive statistics and elementary probability. The core of this topic involves understanding how to summarize a group of numbers using measures like the arithmetic mean, median, mode, and range. Furthermore, students must grasp measures of dispersion, such as standard deviation and interquartile range, which describe how spread out the data points are from the average. The normal distribution, often referred to as the bell curve, is a critical concept where data is symmetrically distributed around the mean. For comprehensive preparation, students often utilize a GRE Prep hub to organize their study of these quantitative concepts. Beyond simple calculations, the GRE tests your ability to analyze how adding or removing a data point affects these statistical measures, a skill that is vital for the Quantitative Comparison and Data Interpretation question types.

Solved Examples

1. Problem: A set of five integers has a mean of 12 and a median of 10. If the smallest integer is 6 and the largest is 20, what is the sum of the remaining two integers?
   Solution:
   1. Calculate the total sum of the five integers using the mean: $5 \times 12 = 60$.
   2. Subtract the known values (smallest and largest) from the total: $60 - 6 - 20 = 34$.
   3. Identify the median's role. Since there are 5 numbers, the median (10) is the 3rd number when ordered.
   4. The sum of the remaining two numbers (the 2nd and 4th numbers) is 34. However, the question asks for the sum of the "remaining two" after removing the smallest, largest, and median. Wait, the remaining two are simply the numbers not already specified.
   5. Total sum is 60. Knowns: 6, 20, and 10. Sum of the two unknown numbers: $60 - (6 + 20 + 10) = 24$.
2. Problem: If the standard deviation of a set $\{x, y, z\}$ is $s$, what is the standard deviation of the set $\{x+5, y+5, z+5\}$?
   Solution:
   1. Recall the property of standard deviation: adding a constant to every term in a set does not change the spread of the data.
   2. The mean increases by 5, but the distance of each point from the new mean remains identical to the original distances.
   3. Therefore, the standard deviation remains $s$.
3. Problem: In a normal distribution, approximately what percent of the data falls within 2 standard deviations of the mean?
   Solution:
   1. Refer to the Empirical Rule (68-95-99.7 rule) commonly taught in statistics and probability courses.
   2. 1 standard deviation covers ~68%.
   3. 2 standard deviations cover ~95%.
   4. The answer is 95%.

Practice Questions

1. A list of numbers consists of: 3, 8, 12, 12, 15, 20. What is the difference between the mean and the median of this list?

2. Set A contains 7 numbers with a mean of 20. Set B contains 3 numbers with a mean of 30. What is the mean of the combined set of 10 numbers?

3. If the range of a set of 10 integers is 25 and the smallest integer is -5, what is the largest possible value in the set?

4. A data set has a standard deviation of 0. Which of the following must be true? (A) The mean is 0. (B) All numbers in the set are identical. (C) The median is 0. (D) The range is 1.

5. A set of numbers is $\{2, 4, 6, 8, 10, 12\}$. If the number 14 is added to the set, which measure will increase the most: Mean, Median, or Mode?

6. In a group of 50 students, the average score on a test was 75. If the 10 students who scored the lowest are removed, the new average becomes 80. What was the average score of the 10 students who were removed?

7. For a set of 5 distinct positive integers, the median is 15 and the mean is 20. What is the maximum possible value for the largest integer in the set?

8. The interquartile range (IQR) of a data set is 15. If the first quartile ($Q_1$) is 20, what is the value of the third quartile ($Q_3$)?

9. A probability experiment has a 0.4 chance of success. If the experiment is performed twice, what is the probability of at least one success? You can use an AI Question Generator to practice similar probability-based statistics problems.

10. The heights of a population are normally distributed with a mean of 170 cm and a standard deviation of 10 cm. What percentage of the population is taller than 190 cm?

Answers & Explanations

1. Answer: 0.33. The sum is $3+8+12+12+15+20 = 70$. Mean = $70/6 = 11.67$. The median is the average of the two middle terms (12 and 12), which is 12. Difference: $12 - 11.67 = 0.33$.
2. Answer: 23. Total sum of A = $7 \times 20 = 140$. Total sum of B = $3 \times 30 = 90$. Combined sum = 230. Combined mean = $230 / 10 = 23$.
3. Answer: 20. Range = Max - Min. $25 = \text{Max} - (-5)$. $25 = \text{Max} + 5$, so Max = 20.
4. Answer: All numbers in the set are identical. Standard deviation measures spread. If there is no spread (SD = 0), all values must be the same distance from the mean (zero distance).
5. Answer: Mean. Original mean = 7, Median = 7. New set $\{2, 4, 6, 8, 10, 12, 14\}$: New mean = 8, New median = 8. Both increased by 1. However, in many skewed additions, the mean is more sensitive to outliers than the median. In this specific arithmetic sequence, they increase equally, but the mode remains non-existent.
6. Answer: 55. Total points = $50 \times 75 = 3750$. Remaining points = $40 \times 80 = 3200$. Points of removed students = $3750 - 3200 = 550$. Average of removed = $550 / 10 = 55$.
7. Answer: 52. Total sum = $5 \times 20 = 100$. To maximize the largest number, minimize the others. Let the set be $\{a, b, 15, d, e\}$. Distinct positive integers: $a=1, b=2$. Since $d > 15$, let $d=16$. Sum = $1+2+15+16+e = 34+e$. $34+e = 100 \Rightarrow e = 66$. (Corrected logic: $1+2+15+16+66 = 100$).
8. Answer: 35. IQR is defined as $Q_3 - Q_1$. $15 = Q_3 - 20$, so $Q_3 = 35$.
9. Answer: 0.64. Probability of at least one success = 1 - P(no successes). P(failure) = $1 - 0.4 = 0.6$. P(two failures) = $0.6 \times 0.6 = 0.36$. $1 - 0.36 = 0.64$.
10. Answer: 2.5%. 190 cm is 2 standard deviations above the mean ($170 + 2 \times 10$). Since 95% of data is within 2 SD, 5% is outside. Half of that 5% is in the upper tail, so 2.5% are taller than 190 cm.

1. If the mean of a set of 6 numbers is 10, and a 7th number, 24, is added, what is the new mean of the set?

• A10
• B12
• C14
• D17

Frequently Asked Questions

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

The mean is the arithmetic average calculated by dividing the total sum by the number of terms, while the median is the middle value when the data is ordered. The GRE often tests these together to see if you understand how outliers pull the mean away from the median.

How is standard deviation calculated for the GRE?

You rarely have to calculate the exact standard deviation using the complex formula on the GRE. Instead, you need to understand that it measures how far data points are from the mean and how adding or shifting data affects that spread.

What is a weighted average and when do I use it?

A weighted average is used when different groups in a set contribute differently to the total, such as two classes of different sizes. You multiply each value by its corresponding weight (or frequency) before summing and dividing by the total count.

Does the GRE provide a formula sheet for statistics?

No, the GRE does not provide a formula sheet, so you must memorize basics like the mean formula, the range, and the properties of the normal distribution. Familiarizing yourself with these through effective practice methods can help with retention.

What are quartiles in GRE data analysis?

Quartiles divide a ranked data set into four equal parts, with Q1 being the 25th percentile, Q2 the median (50th), and Q3 the 75th percentile. They are primarily used to calculate the interquartile range and to create boxplots.