Statistics and Probability
What you must understand
This domain covers data displays, measures of center and spread, probability rules, conditional probability, and sampling. Know when mean or median better represents a data set, how outliers affect each, and how standard deviation measures spread. For probability, distinguish independent from dependent events, use the multiplication and addition rules correctly, and interpret two-way tables.
Traps that appear in questions
- Independent vs dependent. P(A and B) = P(A)·P(B) only when events are independent; otherwise use P(A)·P(B|A).
- "Or" vs "and." For "or," add and subtract the overlap: P(A) + P(B) − P(A and B).
- Median with even counts. Average the two middle values.
- Outlier effects. The mean shifts toward outliers; the median resists them.
- Sampling bias. A voluntary-response or convenience sample may not represent the population.
Worked example
A bag has 4 red and 6 blue marbles. Draw two without replacement. P(both red) = (4/10)(3/9) = 12/90 ≈ 0.133. Because the first draw changes the composition, the events are dependent. Rule of thumb: ask whether earlier outcomes change later probabilities; if yes, adjust the denominator.
Two-way tables
Compute conditional probability by restricting to the row or column of the given condition. Read carefully whether the question asks for a joint or conditional probability.