Statistics and probability
Statistics and probability
Statistics questions test interpretation as much as calculation. You must read tables, bar and line graphs accurately and notice truncated axes or unusual scales; choose and compute mean, median, mode and range; and know that the mean is pulled by outliers while the median resists them. With an even number of values the median is the average of the two middle values, so order the data first. Categorical data is summarised with counts and percentages; numerical data supports averages.
Probability is a long-run relative frequency on a scale from 0 to 1. Use the complement: P(not A) = 1 − P(A), which is the fastest route for "at least one" questions. For independent events, multiply probabilities; for mutually exclusive events, add them. Expected frequency = probability × number of trials. In two-way tables, decide whether a percentage should be taken out of the row total, the column total or the grand total before dividing.
Traps: forgetting to order data before finding the median; reporting impossible averages such as 3.67 people; confusing "at least one" with "exactly one"; treating correlation as proof of causation; and drawing strong conclusions from a tiny or biased sample.
Worked example. For the data 4, 7, 7, 9, 13, 20: the mean is 60 ÷ 6 = 10; ordered, the middle two are 7 and 9, so the median is 8; the mode is 7; the range is 16. The mean sits above the median because 20 is an outlier.