Statistics and Probability
Statistics and Probability
Candidates should summarise data with mean, median, mode, range, quartiles, and interquartile range, and interpret tables, histograms, and box plots. Know the difference between discrete and continuous data and between a population and a sample. For probability, use the complement rule, the addition rule, and the multiplication rule for independent events; understand conditional probability and sampling without replacement.
Traps: forgetting to order data before finding the median; misreading an even-sized data set where the median is the mean of the two middle values; and assuming the mean is resistant to outliers. In probability, 'at least one' is usually easiest via 1 − P(none). Do not add probabilities of events that are not mutually exclusive without subtracting the overlap. With draws without replacement, the denominator changes after each draw. Distinguish independent events from mutually exclusive events.
Rule of thumb: for 'at least one', find the probability of none and subtract from 1. For without-replacement problems, reduce both the favourable count and the total count after each draw.
Worked example: a bag has 3 red and 2 blue counters. Two are drawn without replacement. P(both red) = (3/5) × (2/4) = 6/20 = 3/10. The second denominator is 4 because one counter has already been removed.