Statistics and Probability
What the domain tests
Statistics and probability tests summary of data, including grouped frequency tables, measures of spread, and probability of combined events. MSCE Additional Mathematics expects a clear sample space or formula statement, exact fractions where possible, and sensible interpretation of the final value.
Core rules
- For grouped data with midpoint x and frequency f: mean x̄=Σfx/Σf. Variance=Σf(x-x̄)^2/Σf=Σfx^2/Σf-(x̄)^2.
- The median class is found from cumulative frequency; the median is the value with cumulative frequency N/2.
- Probability P(A)=favourable outcomes/equally likely outcomes. P(A')=1-P(A). P(A∪B)=P(A)+P(B)-P(A∩B).
- Independent events: P(A∩B)=P(A)P(B). Mutually exclusive events have P(A∩B)=0.
- For without-replacement selections, update the denominator and the numerator after each draw.
Worked example
A bag has 4 red and 6 blue counters. Two are drawn without replacement. Find P(both red). P(first red)=4/10. After one red is removed, 3 red remain among 9 counters, so P(second red|first red)=3/9. Therefore P(both red)=4/10×3/9=12/90=2/15.
Traps
Using class limits instead of midpoints; forgetting to subtract P(A∩B) in the union formula; treating without-replacement draws as independent; rounding probabilities before simplifying.