Counting and introductory statistics.
Count arrangements and selections accurately, summarise real data, judge samples and use normal models thoughtfully.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Multiplication principle
Count a sequence of choices by tracking how many choices are possible at each stage.
- 02
Factorials
Use factorial notation to describe descending products and simplify expressions before calculating.
- 03
Permutations
Count ordered selections, including restrictions that change the number of legal arrangements.
- 04
Combinations
Count unordered groups and use casework when a selection has conditions.
- 05
Pascal's triangle and finite binomial expansion
Use Pascal coefficients and combinations to expand finite powers and identify a particular term.
- 06
Discrete versus continuous data
Recognise whether data arise from counting, measuring or categories, and match displays to the recorded variable.
- 07
Samples and populations
Define the group being studied and design a sample that supports a defensible conclusion.
- 08
Mean/median/mode
Calculate common measures of centre and choose a measure that matches the data and purpose.
- 09
Range, quartiles and interquartile range
Describe spread with range and quartiles, and construct a five-number summary using an explicit convention.
- 10
Sample standard deviation
Calculate sample standard deviation and interpret it as a measure of spread around the sample mean.
- 11
Comparing distributions
Compare shape, centre and spread together, then limit conclusions to what the data and sampling support.
- 12
Normal-curve features and the 68–95–99.7 rule
Use symmetry and standard-deviation distances to make approximate probability statements for a normal model.
- 13
Estimating proportions in normal models with appropriate technology
Calculate interval and tail proportions with a normal CDF, and interpret the model rather than just a calculator output.
Topic review
Revisit the key ideas, then choose a practice paper.