Statistics and Probability
Core concepts
You must be able to summarise data with mean, median, mode, range, and interquartile range, read and interpret box plots and histograms, and reason about spread and outliers. For probability, know the complement rule, the addition rule for mutually exclusive events, and the multiplication rule for independent events. Understand that correlation does not imply causation, and recognise sampling bias.
Traps to watch
- Confusing mutually exclusive with independent events.
- Forgetting to find a common denominator when averaging groups of different sizes.
- Reading the median from a histogram as the tallest bar rather than the middle value.
- Assuming events are independent when sampling without replacement.
- Reporting a mean for skewed data when the median is more appropriate.
Worked example
A bag holds 4 red and 6 blue counters. Two are drawn without replacement. The probability both are red is (4/10) × (3/9) = 12/90 = 2/15. The second draw is conditional, so the denominator drops to 9.
Rule of thumb
Before multiplying probabilities, ask whether the first outcome changes the second. If it does, adjust the denominator.