Statistics and Probability
Statistics and Probability tests summarising data - mean, median and mode - and assigning classical probabilities. Grouped-data questions reward careful table reading.
Core rules
- Mean of raw data = sum of observations/number of observations.
- For grouped data, mean = Σfᵢxᵢ/Σfᵢ, where xᵢ is the class mark. The assumed-mean method uses deviations from a chosen value.
- Median of ordered raw data: the middle value when n is odd, and the average of the two middle values when n is even.
- For grouped data, median = l + [(n/2 − cf)/f] × h, with l the lower limit of the median class, cf the cumulative frequency before it, f its frequency and h the class width.
- Probability of an event E = number of favourable outcomes / total number of equally likely outcomes; 0 ≤ P(E) ≤ 1.
Worked example
A bag has 5 red and 7 blue balls. One ball is drawn at random. Total outcomes = 12; favourable red outcomes = 5, so P(red) = 5/12. The probability of not drawing red is 1 − 5/12 = 7/12, which matches the 7 blue balls.
Traps
The median class is the class where cumulative frequency first reaches or exceeds n/2. Do not use class limits in place of class marks for the mean. Probability cannot be negative or greater than 1. When two events are complementary, their probabilities add to 1 - but only if they are the only possibilities.