Data Analysis

Section: Data Analysis and Statistics 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) =…