Statistics and Probability
What this domain covers
Statistics and Probability is about 20% of the test. Expect to summarize data sets, read graphs and tables, judge sampling and study design, interpret scatterplots, and compute simple and compound probabilities.
Core rules
- Center: mean = sum ÷ count; median = the middle value after ordering, or the average of the two middle values when the count is even; mode = most frequent value.
- Outliers pull the mean toward them while the median resists; in a right-skewed distribution the mean exceeds the median.
- Spread: range = maximum − minimum; IQR = Q3 − Q1; a larger standard deviation means values sit farther from the mean.
- Sampling: random sampling supports generalization to the population; volunteer or convenience samples do not.
- Scatterplots: correlation is not causation, and predicting far beyond the observed data is unreliable.
- Probability: P(event) = favorable outcomes ÷ total outcomes, 0 ≤ P ≤ 1, and P(not A) = 1 − P(A). Independent events multiply; drawing without replacement changes the denominator.
Worked example
A bag holds 5 red and 3 blue marbles, 8 total. Two are drawn without replacement. P(both red) = (5/8) × (4/7) = 20/56 = 5/14, about 0.36. The second fraction uses 4 red out of 7 remaining because the first red marble is gone.
Traps that cost marks
- Taking the median before putting the values in order.
- Using 5/8 twice by ignoring that the draw is without replacement.
- Adding probabilities for events that overlap without subtracting the overlap.
- Concluding a causal relationship from a strong correlation.
- Generalizing from a survey of one club to an entire school.