GRE Quantitative Reasoning Practice: Data Interpretation and Statistics
- Data Interpretation and Statistics
- 15 questions
- 26 minutes
GRE Quantitative Reasoning includes Data Interpretation sets, where several questions share one table or graph. This test has two such sets plus separate questions on mean, median, standard deviation, the normal distribution, probability and counting. In percent questions, check which value is the base before you divide.
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Question 1
Data Set A
Annual sales of a company by region (millions of dollars) Region 2023 2024 North 42 48 South 35 28 East 50 55 West 23 29 Total 150 160 By approximately what percent did the company's total sales increase from 2023 to 2024?
Correct answer: B
Total sales rose by 160 − 150 = 10 million dollars, and 10/150 ≈ 6.7%. Dividing by the 2024 total (10/160 = 6.25%) uses the wrong base.
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Question 2
Data Set A (see above):
Which region had the greatest percent increase in sales from 2023 to 2024?
Correct answer: D
West grew from 23 to 29, an increase of 6/23 ≈ 26%. North also grew by 6 million dollars, but from a larger base (6/42 ≈ 14%), and East grew 5/50 = 10%.
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Question 3
Data Set A (see above):
To the nearest tenth of a percent, what percent of the company's 2024 sales came from the East region?
Correct answer: A
In 2024 the East had 55 of 160 million dollars: 55/160 = 34.375% ≈ 34.4%. The value 36.7% divides by the 2023 total of 150.
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Question 4
Data Set A (see above):
By what percent did sales in the South region decrease from 2023 to 2024?
Correct answer: B
Sales fell by 35 − 28 = 7 million dollars, and 7/35 = 20%. Dividing by the new value 28 gives 25%, but a percent decrease is measured from the original value.
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Question 5
Data Set A (see above):
Suppose West region sales increase from 2024 to 2025 by the same percent as from 2023 to 2024. To the nearest tenth, what would West sales be in 2025, in millions of dollars?
Correct answer: C
The growth factor is 29/23, so 2025 sales would be 29 · 29/23 ≈ 36.6 million dollars. Adding the same 6 million again (35.0) keeps the dollar change constant, not the percent change.
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Question 6
A data set consists of these values: 12, 7, 3, 15, 9, 7, 20, 11.
What is the median of the data set?
Correct answer: C
In order: 3, 7, 7, 9, 11, 12, 15, 20. With 8 values, the median is the mean of the 4th and 5th values: (9 + 11)/2 = 10. The value 10.5 is the mean and 7 is the mode.
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Question 7
Each list below has a mean of 10. Which list has the greatest standard deviation?
Correct answer: D
Standard deviation measures how far the values typically are from the mean. In 1, 10, 10, 19 two values are 9 away from 10, farther than in any other list; 10, 10, 10, 10 has a standard deviation of 0.
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Question 8
The scores on an exam are approximately normally distributed with a mean of 70 and a standard deviation of 8.
Approximately what percent of the scores are between 62 and 86?
Correct answer: C
62 is one standard deviation below the mean and 86 is two above. About 34% of a normal distribution lies within one standard deviation below the mean and about 47.5% within two above, giving about 34% + 47.5% ≈ 82%.
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Question 9
Class A has 20 students with an average score of 80. Class B has 30 students with an average score of 70.
What is the average score of all 50 students combined?
Correct answer: B
The total is 20 · 80 + 30 · 70 = 1,600 + 2,100 = 3,700, and 3,700 ÷ 50 = 74. The simple average of the two class averages, 75, ignores that class B is larger.
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Question 10
A bag contains 4 red marbles and 6 blue marbles. Two marbles are drawn at random without replacement.
What is the probability that both marbles are red?
Correct answer: A
The probability is 4/10 · 3/9 = 12/90 = 2/15. The value 4/25 = (4/10)² would be correct only if the first marble were put back before the second draw.
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Question 11
In how many ways can a committee of 3 people be chosen from a group of 8 people?
Correct answer: B
Order does not matter in a committee, so the count is C(8, 3) = (8 · 7 · 6)/(3 · 2 · 1) = 56. The value 336 counts ordered selections, as if the 3 roles were different.
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Question 12
Data Set B
The bar graph shows how many books each of the 20 members of a reading club read last month.
What is the average (arithmetic mean) number of books read per member?
Correct answer: A
The total is 0 · 3 + 1 · 5 + 2 · 7 + 3 · 4 + 4 · 1 = 35 books, and 35 ÷ 20 = 1.75. The value 7 is the height of the tallest bar (the number of members who read 2 books), not an average.
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Question 13
Data Set B (see above):
What is the median number of books read per member?
Correct answer: D
With 20 members, the median is the average of the 10th and 11th values in order. The first 3 values are 0, the next 5 are 1 (up to the 8th), and the 9th through 15th are 2, so the median is 2. The value 1.75 is the mean, not the median.
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Question 14
Data Set B (see above):
What percent of the members read at least 3 books last month?
Correct answer: C
At least 3 means 3 or 4 books: 4 + 1 = 5 members, and 5/20 = 25%. The value 20% counts only the members who read exactly 3 books.
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Question 15
Each value in a data set is increased by 5.
What happens to the standard deviation of the data set?
Correct answer: A
Adding the same number to every value shifts the mean by 5 as well, so every distance from the mean is unchanged. The spread, and therefore the standard deviation, stays the same.
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