Data Handling and Probability
What this domain tests
Summarising a small data set and computing probabilities from lists, tables or simple experiments.
Core rules
- Mean = sum of values ÷ number of values. A weighted mean weights each value by its frequency.
- Median: order the values first, then take the middle one, or the average of the two middle values when the count is even.
- Mode is the most frequent value; range is maximum minus minimum. The median is resistant to outliers, the mean is not.
- Probability P = favourable outcomes ÷ total equally likely outcomes, always between 0 and 1. The complement rule gives P(not A) = 1 − P(A).
- Independent events: multiply the probabilities. "At least one" is almost always fastest through the complement.
Worked example
Two fair coins are tossed. Find the probability of at least one head. The complement of "at least one head" is "no heads", with probability ½ × ½ = ¼. So P(at least one head) = 1 − ¼ = ¾.
Traps that cost marks
Taking a median without sorting; treating "at least one" as "exactly one"; adding probabilities of events that can happen together; assuming outcomes are equally likely when the table shows they are not; counting a result twice in a two-stage experiment.