Statistics and Probability: Data, Averages and Chance
What you must command
You need to summarise data and reason about chance. Know the mean, median, mode and range, and when each is appropriate; understand quartiles, interquartile range and box plots; read and interpret bar charts, histograms and cumulative frequency curves. Know the probability scale from 0 to 1, the complement rule, mutually exclusive and independent events, and the multiplication and addition rules. Be able to use tree diagrams and two-way tables, and to distinguish experimental from theoretical probability. Sampling, bias and the difference between correlation and causation also appear.
Traps that catch candidates
- The median of an even number of values is the mean of the two middle values after ordering.
- Histogram bars use frequency density, not frequency, when class widths differ.
- Independent events multiply; mutually exclusive events add. Mixing these is the commonest error.
- With replacement and without replacement give different probabilities; read the wording carefully.
- Correlation does not imply causation, whatever the strength of the relationship.
- Probabilities must lie between 0 and 1, and the probabilities of all outcomes sum to 1.
Worked example
A bag holds 3 red and 5 blue counters. Two are drawn without replacement. Probability both red = (3/8) times (2/7) = 6/56, which simplifies to 3/28. The second fraction changes because the bag now holds 7 counters with 2 red ones.
Rule of thumb
Draw the tree or table before calculating, and write whether events are independent or exclusive at the top. The structure usually reveals the correct rule.