Statistics and Probability
Core content
Candidates should summarise data with mean, median, mode, range, quartiles, interquartile range, and standard deviation, and choose appropriate displays. Understand populations and samples, random sampling, bias, and the difference between observational studies and experiments. Probability content includes sample spaces, the addition and multiplication rules, conditional probability, independence, counting techniques, expected value, and the normal distribution.
Trap watch
The mean is sensitive to outliers while the median is resistant. With an even number of ordered values, the median is the average of the two middle values. P(A and B) is not generally P(A) times P(B) unless A and B are independent; conditional probability reverses the conditioning. With sampling without replacement, the denominator changes after each draw. The word or is usually inclusive unless exclusive is stated. Correlation does not establish causation, and a voluntary-response sample is rarely representative.
Worked example
A bag contains 3 red and 2 blue counters. Two are drawn without replacement. P(red then blue) = (3/5)(2/4) = 6/20 = 3/10. The second denominator is 4 because one counter has already been removed.
Rule of thumb: define the events, write the sample space or tree diagram, and update denominators when sampling without replacement.