Probability, Statistics, and Data Analysis
Core content
Statistics questions ask you to summarize and compare data using mean, median, mode, range, interquartile range, and standard deviation, and to read displays such as dot plots, histograms, box plots, and scatterplots. Know how outliers affect measures of center, how to interpret percentiles, and how sampling method affects generalization. Probability questions cover sample spaces, theoretical and experimental probability, complementary events, independent and dependent events, and conditional probability. The multiplication rule for independent events is P(A and B) = P(A)P(B); for dependent events, adjust the second probability.
Traps
Mean is pulled strongly by outliers, while median is resistant. Do not confuse 'and' with 'or': P(A or B) = P(A) + P(B) - P(A and B). With no replacement, the denominator changes on the second draw. A common error is treating dependent events as independent. Also watch graphs with misleading scales or truncated axes, and remember that correlation does not prove causation. A voluntary-response sample is usually biased.
Worked example
A bag has 3 red and 5 blue marbles. Two are drawn without replacement. P(both red) = (3/8)(2/7) = 6/56 = 3/28. If the first marble were replaced, the probability would be (3/8)(3/8) = 9/64, which is different.
Rule of thumb
Before computing probability, ask: are outcomes equally likely, and is sampling with or without replacement?