Data Analysis, Statistics, and Probability
Data Analysis, Statistics, and Probability
This domain tests how data are collected, displayed, summarized, and interpreted, plus basic probability. Expect items on mean, median, mode, range, reading tables and graphs, sampling, and simple and compound probability.
Core rules
- Mean = sum of values ÷ number of values. It uses every value and is pulled toward outliers.
- Median is the middle value after ordering the data; with an even count, average the two middle values. Mode is the most frequent value; a data set can have no mode or several.
- Range = maximum − minimum. It measures spread, not center.
- Probability of an event = favorable outcomes ÷ total equally likely outcomes. The complement rule: P(not A) = 1 − P(A).
- Independent events: P(A and B) = P(A) × P(B). For A or B with mutually exclusive events, add the probabilities; if they overlap, subtract the overlap.
- Sampling: a random sample better represents a population than a convenience sample. Graph scales can exaggerate or hide change.
Worked example
Data: 4, 6, 6, 8, 20. Ordered already. Mean = 44 ÷ 5 = 8.8. Median = 6. Mode = 6. Range = 20 − 4 = 16. The mean is greater than the median because 20 is an outlier pulling the mean upward; the median better describes a typical value here.
Traps
Do not find a median before sorting. Do not call the range a measure of center. Do not add probabilities for events that can happen together without subtracting the overlap. Do not use P(A) × P(B) for dependent events. Do not trust a graph without checking axis labels, units, and scale.