Mathematics - Data Analysis, Probability, and Statistics
What this domain asks you to do
This domain covers reading and building data displays, summarizing data with measures of center and spread, recognizing misleading graphs, sampling and bias, and computing probabilities for simple and compound events.
Concepts to master
- Displays: dot plots, histograms, box plots, stem-and-leaf, scatterplots, and two-way tables - and which summary each display suits.
- Center and spread: mean, median, mode, range, interquartile range, and mean absolute deviation. The mean responds to outliers; the median resists them.
- Sampling: a random sample represents a population; biased samples (convenience, self-selected) do not.
- Probability: P(event) = favorable outcomes ÷ total outcomes; independent events multiply; the probabilities of all outcomes sum to 1.
- Association: scatterplots show positive, negative, or no association, and outliers.
Traps the test sets
Confusing mean and median when an outlier is present; reading a graph whose axis does not start at zero; treating dependent events as independent (drawing without replacement); computing probability as a ratio of the wrong whole; describing association as causation; forgetting that a box plot shows the median, not the mean.
Rule of thumb and worked example
When data are skewed or contain an outlier, report the median and interquartile range; when data are roughly symmetric, the mean and range are informative.
Worked example: a fair coin is flipped twice. The four equally likely outcomes are HH, HT, TH, TT, so P(two heads) = 1/4. Multiplying 1/2 × 1/2 gives the same result because the flips are independent. If a marble is drawn and not replaced, the second draw is dependent, and the denominator must drop by one.