Statistics and Probability
Statistics and Probability
The Statistics and Probability domain asks you to summarize and interpret data, read two-way tables, analyze scatterplots, and use linear models. OST items emphasize interpretation: what a slope, intercept, association, or conditional frequency means in the given context.
Core rules
- For categorical data, use bar charts and two-way tables. Joint frequencies count the intersection; marginal frequencies count totals; conditional relative frequencies divide by a row or column total.
- For quantitative data, describe shape, center, spread, and outliers. The mean is affected by outliers more than the median.
- A scatterplot shows association: positive or negative, linear or nonlinear, strong or weak. Correlation r measures linear strength and direction, not causation.
- The line of best fit y-hat = a + bx predicts y; b is the predicted change in y per one-unit increase in x, and a is the predicted y when x = 0-only meaningful if x = 0 is in context.
Worked example
A survey of 100 students finds that 40 play a sport, 30 play an instrument, and 10 do both. The probability a student plays an instrument given they play a sport is P(instrument | sport) = 10/40 = 0.25. This is a conditional relative frequency, not the joint probability 10/100 = 0.10.
Traps
Using a joint frequency where a conditional is requested; interpreting r = 0.9 as proof that x causes y; extrapolating a line of best fit far beyond the data; and reporting an intercept that has no real-world meaning because x = 0 is outside the observed range.