Statistics and Probability
The Statistics and Probability domain tests the collection, organisation, summary and interpretation of data, together with elementary probability. Questions may require choosing an appropriate average, reading a frequency table, comparing distributions, or calculating probabilities from a described sample space.
Core rules and concepts
- Data are either categorical or numerical; numerical data may be discrete or continuous. A sample must be selected in a way that avoids bias if it is to support a generalisation.
- Mean = sum of values ÷ number of values. Median = middle value when data are ordered; for an even count it is the mean of the two middle values. Mode = most frequent value.
- Range = maximum − minimum. It is a simple measure of spread but is sensitive to outliers.
- Probability is a number from 0 to 1: P(event) = number of favourable outcomes ÷ total number of equally likely outcomes.
- P(not A) = 1 − P(A). For mutually exclusive events, P(A or B) = P(A) + P(B). For independent events, P(A and B) = P(A) × P(B).
- In sampling without replacement, the denominator and the favourable count change after each draw.
Worked example
A bag contains 5 red, 3 blue and 2 green counters. Two counters are drawn without replacement. Find the probability that both are red. First draw: P(red) = 5/10. After one red is removed, 4 red counters remain among 9 counters: P(second red | first red) = 4/9. Therefore P(both red) = (5/10) × (4/9) = 20/90 = 2/9. The multiplication is justified because the second draw is conditional on the first.
Traps that cost marks
- Using the original denominator on a second draw without replacement.
- Finding the median without ordering the data first.
- Averaging grouped data without using class midpoints.
- Adding probabilities of events that are not mutually exclusive.
- Treating P(A and B) = P(A) × P(B) as valid for dependent events.