Statistics and probability
Statistics and probability in SEE Optional Mathematics tests summarising data and computing simple probabilities from equally likely outcomes.
Central tendency and dispersion
For ungrouped data, mean = (Σx)/n. For grouped data with frequencies, mean = (Σfx)/Σf. Median is the middle value after ordering; for even n, average the two middle values. Mode is the most frequent value. Quartiles split ordered data into four parts: Q₁ is the median of the lower half, Q₃ of the upper half; quartile deviation = (Q₃−Q₁)/2. Standard deviation for ungrouped data is σ=√(Σ(x−x̄)²/n); for grouped data use class midpoints.
Probability
Classical probability P(E)=number of favourable outcomes / total equally likely outcomes. P(not E)=1−P(E). For mutually exclusive events, P(A∪B)=P(A)+P(B); for overlapping events, subtract P(A∩B). Independent events satisfy P(A∩B)=P(A)P(B).
Worked example
A bag has 3 red and 5 blue balls. P(red)=3/8. If one ball is drawn and not replaced, then a second is drawn, P(red then blue)= (3/8)(5/7)=15/56.
Traps
Using n rather than n−1 inconsistently in standard deviation when the formula specifies n; forgetting to order data before finding median/quartiles; adding probabilities of non-mutually-exclusive events without subtracting the overlap; treating without-replacement draws as independent.