Easy GRE Statistics Set 1 Practice Questions

Concept Explanation

Statistics on the GRE involves the analysis, interpretation, and presentation of data sets using measures of central tendency and dispersion. At its core, this subject requires you to understand how to summarize a group of numbers into a few key values: the mean (average), median (middle value), mode (most frequent value), and range (difference between the highest and lowest values). For students starting their GRE Prep journey, these concepts form the foundation for more complex data interpretation questions.

The arithmetic mean is calculated by summing all terms in a set and dividing by the number of terms. The median is the value that falls exactly in the center when the data is ordered from least to greatest. If the set has an even number of terms, the median is the average of the two middle numbers. The range provides a simple measure of spread, calculated as $\ \text{Max} - \ \text{Min}$. Understanding these basics is essential before moving on to GRE practice questions with explanations that involve standard deviation or normal distributions.

Solved Examples

1. Finding the Mean: A student takes five exams and receives scores of 85, 90, 75, 80, and 95. What is the average score?
   1. Sum the scores: $85 + 90 + 75 + 80 + 95 = 425$.
   2. Count the number of exams: 5.
   3. Divide the sum by the count: $\ \frac{425}{5} = 85$.
   4. The mean score is 85.
2. Finding the Median: Consider the following set of numbers: $\{12, 5, 22, 30, 7, 12, 18\}$. What is the median?
   1. Arrange the numbers in ascending order: $5, 7, 12, 12, 18, 22, 30$.
   2. Identify the middle position. Since there are 7 terms, the middle term is the 4th term.
   3. The 4th term is 12.
   4. The median is 12.
3. Calculating Range: A small business records its daily sales for a week: $200, $450, $300, $150, $800, $600, and $550. What is the range of the sales?
   1. Identify the maximum value: $800.
   2. Identify the minimum value: $150.
   3. Subtract the minimum from the maximum: $800 - 150 = 650$.
   4. The range is $650.

Practice Questions

1. A set of data consists of the following integers: $\{4, 8, 15, 16, 23, 42\}$. What is the arithmetic mean of this set?

2. In a sequence of 10 consecutive integers, the sum of the first five integers is 100. What is the sum of the next five integers?

3. If the mode of the set $\{x, 3, 7, 3, 9, 7, x\}$ is 7, what is the value of $x$?

4. The weights of five boxes are 12 kg, 15 kg, 18 kg, 20 kg, and $w$ kg. If the average weight of the boxes is 17 kg, what is the value of $w$?

5. A list of numbers consists of $\{2, 10, 14, 6, 8, 10, 4\}$. What is the median of this list?

6. If the range of a set of five distinct positive integers is 10 and the smallest integer is 5, what is the largest possible average for the set?

7. A student's average on 4 tests is 88. What score does the student need on the 5th test to raise the average to 90?

8. Which of the following sets has a median that is equal to its mean? $A = \{1, 2, 6\}, B = \{2, 4, 6\}, C = \{3, 3, 9\}, D = \{0, 5, 10\}$.

9. In a group of 5 people, the ages are 22, 25, 22, 30, and 26. If a 60-year-old person joins the group, which statistical measure will increase the most: mean, median, or mode?

10. A set contains the numbers $\{x, y, z\}$. If the mean is 10 and $x = 5$, what is the sum of $y$ and $z$?

Answers & Explanations

1. Answer: 18. Sum the integers: $4+8+15+16+23+42 = 108$. Divide by the count: $108 / 6 = 18$.
2. Answer: 125. Let the first five be $n, n+1, n+2, n+3, n+4$. Their sum is $5n + 10 = 100$, so $5n = 90$ and $n = 18$. The next five are $23, 24, 25, 26, 27$. Their sum is $23+24+25+26+27 = 125$.
3. Answer: 7. The current counts are two 3s and two 7s. For 7 to be the unique mode, $x$ must be 7, making the count of 7s equal to four.
4. Answer: 20. Use the formula $\ \text{Sum} = \ \text{Average} \ \times \ \text{Count}$. $12+15+18+20+w = 17 \times 5$. $65 + w = 85$, so $w = 20$.
5. Answer: 8. Sort the list: $2, 4, 6, 8, 10, 10, 14$. The middle value (4th term) is 8.
6. Answer: 11.4. Smallest is 5, range is 10, so largest is 15. To maximize the average, make the other three integers as large as possible while staying distinct: 14, 13, 12. Sum: $5+12+13+14+15 = 59$. Average: $59/5 = 11.8$. (Correction: Distinct integers are 15, 14, 13, 12, 5).
7. Answer: 98. Total points for 4 tests: $88 \times 4 = 352$. Total points needed for 5 tests: $90 \times 5 = 450$. Required score: $450 - 352 = 98$.
8. Answer: B and D. For B: Mean = $(2+4+6)/3 = 4$; Median = 4 (Equal). For D: Mean = $(0+5+10)/3 = 5$; Median = 5 (Equal).
9. Answer: Mean. The original mean is 25. The new mean is $(125+60)/6 = 30.83$ (increase of 5.83). The median moves from 25 to 25.5. The mode remains 22. The mean is most sensitive to outliers.
10. Answer: 25. Mean of 3 numbers is 10, so the sum is $10 \times 3 = 30$. If $x + y + z = 30$ and $x = 5$, then $y + z = 25$.

1. If a set of data is {2, 2, 4, 8, 14}, what is the arithmetic mean?

• A4
• B5
• C6
• D8

Frequently Asked Questions

What is the difference between mean and median?

The mean is the calculated average of all values in a set, whereas the median is the physical middle value when the set is ordered. The mean is sensitive to outliers, while the median provides a better measure of the center for skewed data.

How do you find the median of an even number of terms?

To find the median for a set with an even number of elements, you must identify the two middle terms and calculate their arithmetic average. For example, in the set {2, 4, 6, 8}, the median is (4 + 6) / 2 = 5.

Can a set have more than one mode?

Yes, a data set can be bimodal or multimodal if multiple values appear with the same highest frequency. If every value appears only once, the set is often described as having no mode.

Does the GRE provide a calculator for statistics questions?

Yes, the GRE provides an on-screen calculator for the Quantitative Reasoning section, which you can use for basic arithmetic like summing values for a mean. You can learn more about test rules via ETS official guidelines.

What is the range of a set with only one number?

The range of a set with only one number is 0 because the maximum and minimum values are identical. Range measures spread, and a single-point set has no spread.