Data Analysis — GRE General Questions

6 GRE General practice questions on Data Analysis, part of Quantitative Reasoning. Below are 6 of them in full, each with the answer and a written explanation.

Questions & explanations

1. When events are independent, P(A and B) = P(A)*P(B). But never assume independence unless stated or obvious (like coin flips). For dependent events, use conditional multiplication.

Trap: In a family with two children, P(both boys) is not 1/4 if we know at least one is a boy? Actually it is 1/3 because the sample space is {BB, BG, GB}. Independence assumption would give 1/4, but the condition changes the sample space.

2. In conditional probability, rewrite the condition as a restriction on the sample space. For 'given that', reduce the total outcomes to only those satisfying the condition.

Example: Two dice rolled, find P(sum > 8 | first die is 5). Restrict to outcomes where first=5: (5,1)...(5,6). Among these, count those with sum>8: (5,4),(5,5),(5,6) => 3/6 = 1/2.

3. Strategy: When a problem involves a missing value given the mean, set up the sum equation. For example, if the mean of n numbers is M, then sum = n*M. Use this to find the missing value.

This technique is straightforward but often overlooked. Always compute total sum from mean and count, then subtract known values.

4. The binomial distribution gives the probability of exactly k successes in n independent trials, each with success probability p. The formula is P(X=k) = C(n,k) * p^k * (1-p)^(n-k). The mean is np and standard deviation is sqrt(np(1-p)).

This is a teaching card. The binomial distribution models the number of successes in a fixed number of independent yes/no trials.

5. Strategy: When comparing two distributions, focus on center (mean or median) and spread (standard deviation or range). A smaller standard deviation indicates less variability and a taller peak if normal.

For normal distributions, the standard deviation determines the spread. A larger SD means more spread and a flatter curve.

6. Strategy: For linear transformations, remember: adding a constant changes mean and median but not range or IQR; multiplying by a constant changes all measures of spread (range, IQR, SD) by the absolute value of the constant, and changes mean and median by the same factor.

This is a key concept. For example, if you multiply every number by 3, the range triples; if you add 5, range stays same.

More Quantitative Reasoning topics

This page shows 6 of 6 questions on this topic. The full set, with progress tracking and five agent perspectives per question, is in the JupiteX app — browse the exam catalogue or browse the Learn library.