Statistics and Probability: Data, Spread, and Chance
What this domain tests
This domain asks you to summarize data and reason about uncertainty. Know measures of center (mean, median, mode) and measures of spread (range, interquartile range, standard deviation), and understand how outliers affect each. Be able to read and interpret dot plots, histograms, box plots, and two-way tables. For probability, understand sample spaces, the complement rule $P(\text{not }A)=1-P(A)$, independent events where $P(A\text{ and }B)=P(A)P(B)$, and conditional probability read from a table. Distinguish experimental from theoretical probability, and recognize sampling bias and the difference between correlation and causation.
Traps to watch for
A classic trap is confusing "and" with "or": for mutually exclusive events, add probabilities; for independent events occurring together, multiply. The median requires data in order, and with an even count you average the two middle values. Outliers pull the mean toward them but barely move the median, so questions asking which measure is more representative often favor the median. In two-way tables, conditional probability uses the row or column total as the denominator, not the grand total. Remember that a strong correlation does not prove causation.
Worked example
A bag holds 3 red and 5 blue marbles. Two are drawn without replacement. Find the probability both are red. The first draw: $\tfrac38$. The second draw: $\tfrac27$ since one red is gone. Multiply: $\tfrac38 \times \tfrac27 = \tfrac{6}{56} = \tfrac{3}{28}$. Rule of thumb: for "without replacement," reduce both the numerator and the denominator before multiplying.