Part V Review

Part V at a glance

This review mixes all six Part V chapters: Center and Spread, Study Design and Sampling, Two-Variable Data and Models, Probability, Normal Distributions and Z-Scores, and Statistical Inference. Use it as a timed mixed set, and for every miss, name the chapter before you look at the explanation.

Quick recall

• Center and spread: the mean is pulled toward outliers and toward the long tail of a skewed distribution; the median is the middle value of the ordered list; range is maximum minus minimum; $\text{IQR} = Q_3 - Q_1$.
• Study design: random selection supports generalizing to a population; random assignment in an experiment supports a causal conclusion; voluntary response and convenience samples invite bias; a lurking third variable can explain a correlation.
• Two-variable data: in $y = mx + b$, the slope is the predicted change in $y$ per one-unit increase in $x$; a residual is actual minus predicted; random residual scatter suggests a good model, while a pattern in the residuals signals a missing piece.
• Probability: multiply for independent "and"; add for mutually exclusive "or"; subtract the overlap otherwise; $P(A \text{ and } B) = P(A) \cdot P(B \mid A)$; combinations when order is irrelevant, permutations when it matters; expected value is the sum of outcome times probability, with losses negative.
• Normal distributions: $z = \frac{x-\mu}{\sigma}$ and $x = \mu + z\sigma$; the empirical rule gives 68%, 95%, and 99.7% for 1, 2, and 3 standard deviations.
• Inference: plausible interval is estimate $\pm$ margin of error; a larger sample narrows the margin of error but does not cure bias; a rare result under a claim is evidence against that claim.

The most common Part V mistakes are mixing up a row total with the grand total, dropping a sign on a residual or z-score, and picking the wrong tail. Slow down on those three.