Statistics and Probability
What this domain tests
Statistics tests mean, median and mode of grouped data and the reading of cumulative-frequency curves. Probability tests classical probability with dice, cards, bags and spinner-type equally likely outcomes.
Core rules
- Grouped mean: direct method Σfx/Σf; assumed-mean method a + Σfd/Σf; step-deviation method a + h(Σfu/Σf).
- Median of grouped data: median = l + [(n/2 − cf)/f] × h, where l is the lower boundary of the median class, cf is the cumulative frequency before it, f is its frequency and h is the class width.
- Mode of grouped data: mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h.
- Probability: P(E) = number of favourable outcomes / total number of equally likely outcomes.
- 0 ≤ P(E) ≤ 1; P(E) + P(not E) = 1; an impossible event has probability 0.
Worked example
A bag contains 5 red and 3 blue balls. One ball is drawn at random. Find P(red) and P(not red). Total balls = 8. P(red) = 5/8. P(not red) = 1 − 5/8 = 3/8, which also equals the 3 blue balls out of 8.
Traps
- Using frequency instead of cumulative frequency when locating the median class.
- Choosing the median class by the largest frequency rather than by n/2.
- Forgetting to add the lower boundary l in the median and mode formulas.
- Counting outcomes that are not equally likely.
- Reporting a probability greater than 1.