Statistics and Probability
What you must understand
Statistics requires you to collect, organise, summarise and interpret data. You must be able to read and construct tables, bar charts, pie charts, histograms and cumulative frequency curves, and to calculate the mean, median, mode and range for raw data, frequency tables and grouped data (using midpoints). You should also understand probability as a number between 0 and 1, use the probability scale, calculate theoretical and experimental probabilities, use tree diagrams and Venn diagrams, and recognise mutually exclusive and independent events.
Traps that appear in questions
- Grouped data. The mean from a grouped table is an estimate using class midpoints.
- Median from a table. Locate the correct position using cumulative frequency, not the middle row.
- Pie chart angles. Each category's angle = (frequency ÷ total) × 360°.
- Probability complement. P(not A) = 1 − P(A).
- Without replacement. The denominator and numerator both change on the second draw.
- Mutually exclusive versus independent. Mutually exclusive events cannot occur together; independent events do not influence each other.
Worked example
A bag holds 4 red and 6 blue counters. Two are drawn without replacement. P(both red) = (4/10) × (3/9) = 12/90 = 2/15. The second fraction uses 9 counters and 3 reds because one red has already been removed.
Rule of thumb
Before calculating any probability, write down the total number of outcomes; then decide whether the events are combined with and (multiply) or or (add, if mutually exclusive).