Statistics, Probability, and Data Analysis
This domain covers descriptive statistics (mean, median, mode, range, standard deviation, quartiles, outliers), data displays (histograms, box plots, scatterplots), sampling and study design, and probability including conditional probability, independence, and counting. You should interpret center, spread, and shape, and distinguish correlation from causation.
Traps to watch
- Mean vs. median under skew: outliers pull the mean but not the median; skewed data is often better summarized by the median.
- Conditional probability: $P(A\mid B) = P(A\cap B)/P(B)$, which is not the same as $P(B\mid A)$. For independent events, $P(A\cap B)=P(A)P(B)$.
- "At least one": use the complement, $1 - P(\text{none})$.
- Sampling bias: a voluntary-response or convenience sample is not representative, regardless of size.
Worked example / rule of thumb
A bag has 4 red and 6 blue marbles. Draw two without replacement. What is the probability both are red? $P = \dfrac{4}{10}\cdot\dfrac{3}{9} = \dfrac{12}{90} = \dfrac{2}{15}$. Rule of thumb: for "without replacement," the denominator shrinks after each draw. For "at least one" events, compute the complement and subtract from 1. When comparing data sets, report both a measure of center and a measure of spread; standard deviation measures typical distance from the mean, so a larger value means more variability.