Statistics and Probability
What the domain tests
Statistics questions test mean, median and mode for grouped data, including the median class formula. Probability questions test classical probability for equally likely outcomes and simple complementary events.
Core rules and concepts
- Mean of grouped data: use class marks with direct method, or deviations with assumed mean.
- Median for grouped data: median = l + [(N/2 − cf)/f] × h, where l is the lower limit of the median class, cf is the cumulative frequency before it, f is its frequency, and h is the class width.
- Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h.
- Probability of an event E is P(E) = number of favourable outcomes / total equally likely outcomes, with 0 ≤ P(E) ≤ 1.
- P(not E) = 1 − P(E).
Worked example
Class intervals 0–10, 10–20, 20–30, 30–40 have frequencies 4, 6, 10, 4. Total N = 24, so N/2 = 12. The cumulative frequencies are 4, 10, 20, 24, so the median class is 20–30. Here l = 20, cf = 10, f = 10 and h = 10. Median = 20 + [(12 − 10)/10] × 10 = 20 + 2 = 22.
Traps that cost marks
Use the cumulative frequency before the median class, not the frequency of the median class. Do not count the same outcome twice in probability. For a die, P(even) = 3/6 = 1/2; for a bag with 3 red and 5 blue balls, P(red) = 3/8, not 3/5.