Statistics and Probability
Overview
Statistics and Probability assesses data collection and presentation, averages and spread, scatter graphs, probability rules and diagrams. CCEA expects candidates to interpret results in context, compare distributions and justify conclusions, not just calculate.
Core rules
- Mean = total of values ÷ number of values. From a frequency table, use Σfx ÷ Σf.
- For grouped data, use class midpoints; the mean is an estimate. The median lies in the class containing the (n+1)/2th value.
- Cumulative frequency is plotted at class upper bounds; a box plot shows median, quartiles and extremes.
- Histogram bar area represents frequency; frequency density = frequency ÷ class width.
- Probability: P(not A) = 1 − P(A). For mutually exclusive events, add probabilities. For independent events, multiply.
- On a tree diagram, multiply along branches and add between branches. Without replacement, the denominator changes after the first pick.
- Correlation describes a relationship on a scatter graph; it does not prove causation.
Worked example
A bag contains 5 red and 3 blue counters. Two counters are taken without replacement. Find P(both red). First pick: P(red) = 5/8. After removing one red, 4 red remain out of 7 counters, so second pick P(red) = 4/7. Multiply: 5/8 × 4/7 = 20/56 = 5/14. The denominator changes because the first counter is not replaced.
Traps
Using the original denominator on the second pick without replacement; plotting cumulative frequency at midpoints rather than upper bounds; treating histogram height as frequency; adding probabilities of non-mutually-exclusive events without subtracting the overlap; claiming causation from correlation.