What you need to know
Statistics and probability questions are usually less about memorising formulas and more about choosing a suitable measure, reading data accurately and communicating what a result means in context.
- Calculate and compare mean, median, mode and range.
- Interpret tables, charts and cumulative data carefully.
- Use probabilities between 0 and 1 and the total probability of all outcomes as 1.
- Use complements and tree diagrams when events have several stages.
Key mathematics
Mean
\bar{x}=\frac{\sum x}{n}
For frequency data, use the sum of fx divided by the sum of f.Complement
P(A^c)=1-P(A)
Useful for “not A” or “at least one” strategies.Worked example
If the probability of a success is 0.35, then the probability of failure is $$1-0.35=0.65.$$ For independent repeated trials, multiply along a branch of a probability tree.
EXAM TECHNIQUE
Exam tips
- Write probabilities on every branch before multiplying.
- For grouped data, remember calculated means are estimates because class midpoints are used.
- When comparing data sets, discuss both a measure of centre and a measure of spread where appropriate.
WATCH OUT
Common mistakes
- Allowing probabilities to add to more than 1 for a complete set of outcomes.
- Using class boundaries incorrectly in grouped-data questions.
- Comparing two distributions using only the mean and ignoring variation.
Frequently asked questions
What is the difference between mean and median?
The mean uses every value; the median is the middle value when data is ordered and is less affected by extreme values.
When should I use the complement rule?
It is often faster for “not”, “none” or “at least one” events.
Why are grouped-data means estimates?
The exact individual values are unknown, so class midpoints are used as representative values.