Estimated study time: 45 minutes
Content:
Data Analysis is one of the four content areas tested in GRE Quantitative Reasoning and covers descriptive statistics, probability, distributions, data interpretation (charts and tables), and combinatorics. Questions requiring data interpretation appear frequently and require reading graphs, tables, and charts accurately before performing calculations.
Descriptive statistics: The mean (arithmetic average) = sum of values / number of values. The median is the middle value when data is ordered — for an even number of values, it is the average of the two middle values. The mode is the most frequent value. Mean is sensitive to outliers; median is robust. The range = max − min. Standard deviation measures spread: higher standard deviation means more dispersion. Variance = (standard deviation)². For the GRE, you need to understand how adding or multiplying all values by a constant affects measures of center and spread: adding constant k to all values increases mean and median by k but does not change standard deviation. Multiplying all values by k multiplies mean, median, and standard deviation by k (variance by k²).
Probability: P(A) = number of favorable outcomes / total outcomes (for equally likely events). Key rules: P(A or B) = P(A) + P(B) − P(A and B) (addition rule). P(A and B) = P(A) × P(B|A) (multiplication rule). For independent events, P(A and B) = P(A) × P(B). Complementary rule: P(not A) = 1 − P(A). The GRE does not test conditional probability theorems like Bayes' theorem in depth — but understanding P(A|B) = P(A and B) / P(B) may be needed.
Counting and combinatorics: Permutations count arrangements where order matters: P(n,r) = n! / (n−r)!. Combinations count selections where order doesn't matter: C(n,r) = n! / [r!(n−r)!]. The GRE frequently asks "how many ways can you choose/arrange k items from n?" — identify whether order matters. Common traps: circular arrangements (divide by n to remove rotational duplicates); arrangements with identical items (divide by the factorial of repeated item count).
Distributions: For a normal distribution, roughly 68% of data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. The GRE doesn't require z-table lookup, but understanding the 68-95-99.7 rule and the symmetric properties of the normal distribution is essential. For discrete distributions, the GRE may test expected value: E(X) = Σ [x × P(x)].
Data interpretation: GRE data interpretation questions present a set of charts or tables followed by 2-3 questions. Read the axis labels, units, and titles carefully before answering — a common error is misidentifying the unit (thousands vs. millions) or reading the wrong bar/line. Watch for questions asking about percent change versus absolute change — these are often traps.
Key Terms:
Quiz Questions:
Q1. A dataset has a mean of 50 and a standard deviation of 10. Every value in the dataset is multiplied by 3. What are the new mean and standard deviation?
A) Mean = 50, Standard deviation = 30 B) Mean = 150, Standard deviation = 30 C) Mean = 150, Standard deviation = 10 D) Mean = 150, Standard deviation = 13
Answer: B — Multiplying every value by 3 multiplies both the mean and the standard deviation by 3: new mean = 50 × 3 = 150; new standard deviation = 10 × 3 = 30. Adding a constant would shift the mean but not affect standard deviation — but multiplying affects both.
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Q2. A bag contains 4 red marbles and 6 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?
A) 4/10 × 4/10 = 16/100 B) 4/10 × 3/9 = 12/90 = 2/15 C) 4/10 × 4/9 = 16/90 D) C(4,2) / C(10,2) = 6/45 = 2/15
Answer: B (and D, same value) — P(1st red) = 4/10. P(2nd red | 1st was red) = 3/9 (without replacement). P(both red) = 4/10 × 3/9 = 12/90 = 2/15. Equivalently: C(4,2)/C(10,2) = 6/45 = 2/15. Both approaches yield 2/15.
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Q3. How many ways can a committee of 3 people be chosen from a group of 8?
A) 336 B) 56 C) 24 D) 512
Answer: B — Order doesn't matter for committee selection: C(8,3) = 8! / (3! × 5!) = (8 × 7 × 6) / (3 × 2 × 1) = 336 / 6 = 56.
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Q4. A fair six-sided die is rolled twice. What is the probability of rolling an even number on the first roll and a number greater than 4 on the second roll?
A) 1/2 B) 1/6 C) 1/3 D) 1/4
Answer: B — P(even on 1st roll) = 3/6 = 1/2. P(>4 on 2nd roll) = 2/6 = 1/3 (outcomes: 5, 6). Rolls are independent: P(both) = 1/2 × 1/3 = 1/6.
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Q5. In a data interpretation question, a bar chart shows Company X had $2.4 million in revenue in 2020 and $3.0 million in 2022. What was the percent change in revenue from 2020 to 2022?
A) 0.6% B) 20% C) 25% D) 80%
Answer: C — Percent change = (New − Old) / Old × 100% = (3.0 − 2.4) / 2.4 × 100% = 0.6 / 2.4 × 100% = 25%. Common trap: dividing by the new value (3.0) gives 20%, which is wrong — always divide by the original (old) value.
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