Statistics and Probability
Core skills
This domain tests summary statistics (mean, median, mode, range, and the meaning of standard deviation), reading data displays such as tables, histograms, box plots, and scatterplots, basic probability for single and compound events, counting with the multiplication principle and with permutations versus combinations, conditional probability, expected value, and the logic of sampling and study design.
Traps to expect
- Median with an even number of values is the average of the two middle values after sorting - and sorting is required first.
- Outliers move the mean, not the median. A question asking which measure is resistant is asking about the median.
- "And" versus "or": multiply for independent events occurring together; add for mutually exclusive alternatives, subtracting any overlap.
- Without replacement changes the denominator on the second draw.
- "At least one" is almost always fastest as $1 - P(\text{none})$.
- Correlation is not causation, and a sample must be random to support generalization.
Worked example
A bag holds 4 red and 6 blue marbles. Two are drawn without replacement. The probability both are red is $\frac{4}{10} \times \frac{3}{9} = \frac{12}{90} = \frac{2}{15}$. If the first marble were replaced, the second factor would stay $\frac{4}{10}$ and the answer would be $\frac{4}{25}$ - a favorite distractor pair.
Rule of thumb
Before computing any probability, state the sample space and whether draws are independent. Writing "with" or "without replacement" at the top of your scratchwork prevents the most common error in this domain.