Data Interpretation, Probability, and Statistics
What this domain tests
Data interpretation, probability, and statistics questions ask you to read tables and graphs, summarize a data set, and compute probabilities. You need to distinguish a count from a rate, a mean from a median, and independent from dependent events.
Core rules
- Mean = sum of values / number of values. Median is the middle value when ordered; with an even count, average the two middle values. Mode is the most frequent value; range = maximum - minimum.
- A weighted mean weights each value by its frequency or group size.
- Probability of an event = favorable outcomes / total outcomes, assuming equally likely outcomes.
- P(A or B) = P(A) + P(B) - P(A and B). For mutually exclusive events, the overlap is zero.
- P(A and B) = P(A) x P(B given A). For independent events, P(B given A) = P(B).
- The probability of at least one occurrence is often easiest as 1 - P(none).
Worked example
A bag contains 5 red, 3 blue, and 2 green marbles. Two are drawn without replacement. P(red then blue) = (5/10) x (3/9) = 15/90 = 1/6. The second denominator is 9 because one marble has already been removed; replacing it would give (5/10)(3/10) = 3/20 instead.
Traps
Without replacement changes the denominator. The median of 2, 4, 6, 8 is (4 + 6)/2 = 5, not 4 or 6. A graph with a truncated axis can exaggerate differences; read the scale. Probability cannot exceed 1, so an answer like 1.2 signals an error. In a two-way table, condition on the row or column total named after the word given.