Practice Data Analysis questions for the Graduate Record Examinations. Every question includes a full explanation of why the correct answer is right and why the tempting distractors are wrong.
10 example questions with full explanations. Use the interactive practice above to work through the complete set.
Question 1medium
A data set contains seven values: 4, 6, 6, 8, 9, 11, 20. Which of the following correctly orders the mean, median, and mode of the data set from least to greatest?
- A.median < mode < mean
- B.mean < median < mode
- C.mode < median < mean✓
- D.mode < mean < median
Correct answer: C
First, identify each measure: the mode is 6 (appears twice), the median is the 4th value in the ordered list = 8, and the mean is (4+6+6+8+9+11+20)/7 = 64/7 ≈ 9.14. So the order from least to greatest is mode (6) < median (8) < mean (~9.14), making C correct. The outlier value of 20 pulls the mean above the median, a classic skew-right pattern. Distractors A and D are wrong because they misplace either the median or mean relative to the mode.
Question 2medium
The eight values below represent the number of hours eight employees spent in training last month, listed in ascending order:
3, 7, 9, 12, 15, 18, 22, 28
What is the interquartile range (IQR) of this data set?
Correct answer: D
For 8 ordered values, Q1 is the median of the lower half {3, 7, 9, 12} = (7+9)/2 = 8, and Q3 is the median of the upper half {15, 18, 22, 28} = (18+22)/2 = 20. The IQR = Q3 − Q1 = 20 − 8 = 12.Acommon error (choice B, 14) results from incorrectly computing Q1 as 9 or Q3 as 23. Choice C (25) is simply the range (28 − 3), confusing range with IQR.
Question 3medium
The table below shows a company's annual revenue (in millions of dollars) from 2018 to 2022.
Year: 2018 | 2019 | 2020 | 2021 | 2022
Revenue: 40 | 52 | 60 | 75 | 85
During which one-year period did revenue increase at the greatest average rate, in millions of dollars per year?
- A.2020 to 2021✓
- B.2018 to 2019
- C.2019 to 2020
- D.2021 to 2022
Correct answer: A
Calculate the year-over-year change in revenue for each period: 2018–2019: 52−40 = +12M; 2019–2020: 60−52 = +8M; 2020–2021: 75−60 = +15M; 2021–2022: 85−75 = +10M. Since each interval is exactly one year, the average rate equals the absolute change, and the largest change is +15M in the 2020–2021 period. Choice C is tempting because 2018–2019 shows a large jump of 12M, but 2020–2021 is still larger. Choice A is the smallest increase.
Question 4medium
The two-way table below shows the beverage preference of 120 people surveyed, categorized by the time of day they prefer to consume it.
| Prefers Coffee | Prefers Tea | Total
Morning person | 45 | 15 | 60
Evening person | 20 | 40 | 60
Total | 65 | 55 | 120
Given that a randomly selected person is a morning person, what is the probability that the person prefers tea?
Correct answer: B
This is a conditional probability question: P(prefers tea | morning person) = (number of morning people who prefer tea) / (total morning people) = 15/60 = 1/4. The condition 'given that the person is a morning person' restricts the sample space to the 60 morning people, not all 120. Choice D (11/24) is a common error from using 55/120, which is the overall proportion of tea drinkers regardless of time preference. Choice B(3/11) mistakenly uses 15 out of the total 55 tea drinkers.
Question 5medium
A bag contains 4 red marbles, 5 blue marbles, and 3 green marbles. Two marbles are drawn at random without replacement. What is the probability that at least one of the two marbles drawn is red?
- A.7/22
- B.1/3
- C.19/33✓
- D.8/11
Correct answer: C
Use the complement rule: P(at least one red) = 1 − P(no red in either draw). The probability of drawing no red marble on the first draw is 8/12, and on the second draw (given the first was not red) is 7/11. So P(no red) = (8/12)(7/11) = 56/132 = 14/33. Therefore P(at least one red) = 1 − 14/33 = 19/33. Choice A (7/22) is the probability of drawing exactly two red marbles: (4/12)(3/11) = 12/132 = 1/11, which is not the same. Choice D (8/11) ignores the dependency between draws by incorrectly treating the draws as independent.
Question 6medium
A company has five employees with annual salaries (in thousands of dollars): 40, 50, 60, 70, and 80. Management decides to give every employee a $10,000 raise. Which of the following correctly describes the effect of this raise on the mean and standard deviation of the salaries?
(Note: standard deviation is calculated using the population formula.)
- A.Both the mean and the standard deviation increase by $10,000.
- B.The mean remains unchanged and the standard deviation increases by $10,000.
- C.Both the mean and the standard deviation remain unchanged.
- D.The mean increases by $10,000 and the standard deviation remains unchanged.✓
Correct answer: D
Adding a constant to every value in a data set shifts the entire distribution by that constant, so the mean increases by $10,000 (from $60K to $70K). However, standard deviation measures spread — the distances between each value and the mean — and those distances are completely unchanged when every value moves by the same amount. Therefore the standard deviation stays the same. Choice A is wrong because SD does not change with a uniform shift. Choices B and C incorrectly keep the mean fixed, which ignores the direct effect of adding a constant to every data point.
Question 7medium
A university's annual operating budget of $6,000,000 is allocated as follows according to a pie chart: Instruction 45%, Research 25%, Administration 20%, and Facilities 10%. A proposal would transfer 5 percentage points of the budget from Administration to Research. After the transfer, how much more money (in dollars) would be allocated to Research than to Facilities?
- A.$1,200,000✓
- B.$900,000
- C.$1,500,000
- D.$1,800,000
Correct answer: A
After the transfer, Research receives 25% + 5% = 30% of the budget, and Facilities remains at 10%. Research allocation = 0.30 × $6,000,000 = $1,800,000. Facilities allocation = 0.10 × $6,000,000 = $600,000. The difference is $1,800,000 − $600,000 = $1,200,000. Choice A($900,000) results from forgetting to apply the transfer and using the original 25% for Research (difference = 20% of $6M × ½, a calculation error). Choice C ($1,500,000) comes from computing 30% − 10% = 20% but then mistakenly applying it to the wrong base. Choice D ($1,800,000) is Research's allocation alone, not the difference.
Question 8medium
A scatterplot displays data for 12 cities, with average daily temperature (°F) on the x-axis and monthly electricity consumption (MWh) on the y-axis. The plotted points follow a pattern in which cities with higher temperatures consistently show higher electricity consumption, with the points clustered tightly around an upward-sloping line of best fit. The correlation coefficient r for this data is most likely which of the following?
- A.r = −0.85
- B.r = 0.90✓
- C.r = −0.10
- D.r = 0.15
Correct answer: B
The scenario describes a strong positive association: as temperature increases, electricity consumption increases, and the points are clustered tightly around the line of best fit.Astrong positive correlation corresponds to an r value close to +1. Therefore r = 0.90 is the best fit. Negative values (A and B) would indicate that higher temperatures correspond to lower consumption — the opposite of what is described. Choice B (r = 0.15) suggests only a very weak positive relationship, inconsistent with points being 'clustered tightly' around the trend line. The tight clustering specifically rules out weak correlations.
Question 9medium
A club must select a president, a vice president, and a treasurer from its 9 members. No member may hold more than one position. In how many different ways can these three positions be filled?
Correct answer: C
Because the three positions are distinct, order matters, making this a permutation problem. The number of ways to fill 3 ordered positions from 9 members is P(9,3) = 9 × 8 × 7 = 504. Option A (84) is the combination C(9,3), which ignores the fact that the positions are distinguishable. Option B (252) is C(9,3) × 3 = 252, a partial but incorrect adjustment. Option D (729) is 9³, which incorrectly allows the same member to hold multiple positions.
Question 10medium
A bag contains 5 red marbles and 3 blue marbles. Two marbles are drawn one at a time without replacement. What is the probability that the first marble drawn is red and the second marble drawn is blue?
- A.15/64
- B.5/18
- C.8/15
- D.15/56✓
Correct answer: D
This is a compound probability problem without replacement. The probability that the first marble is red is 5/8. After removing one red marble, 7 marbles remain (4 red, 3 blue), so the probability the second is blue is 3/7. The combined probability is (5/8) × (3/7) = 15/56. Option A (15/64) is the result of incorrectly treating the draws as independent (with replacement): (5/8) × (3/8). Option B (5/18) is a common arithmetic error when combining fractions incorrectly. Option C (8/15) results from inverting the fraction or computing the complement.