Statistics and Probability
Statistics and Probability
This domain tests summarising data, interpreting displays, and calculating probabilities. Expect mean, median, mode, range, quartiles, tables, and simple probability rules.
Core rules
- Mean = sum of values ÷ number of values. Median is the middle value after ordering. Mode is the most frequent value.
- Range = maximum - minimum. It measures spread, not centre.
- Probability lies between 0 and 1. 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).
- Conditional probability: P(A|B) = P(A and B)/P(B).
- A two-way table is often the safest way to organise joint and complementary events.
Worked example
A bag has 5 red and 3 blue counters. Two counters are taken without replacement. What is the probability both are red? First red: 5/8. After removing one red, 4 red remain out of 7. Second red: 4/7. Product = 20/56 = 5/14. The without-replacement condition changes the denominator, so the draws are not independent.
Traps
- Using the original denominator after a without-replacement draw.
- Confusing P(A and B) with P(A or B).
- Adding probabilities of overlapping events without subtracting the overlap.
- Choosing the mean when outliers make the median more representative.
- Forgetting to order data before finding the median.