The underlying big ideas forming the foundation for meaningful, context-based statistical investigations are: variation, expectation, distribution, randomness and informal inference.

**Variation** is the term that describes the differences we observe around us in every aspect of life, such as age, height, rainfall, temperature and prices. Variation is first mentioned in year 3 where students are asked to recognise variation in chance outcomes.

**Expectation** arises when we wish to harness variation and summarise data. For example,

- What is the typical price?
- What is the average temperature?
- What is the chance of tossing a head?

It arises throughout the curriculum but is referred to explicitly in year 6.

**Distribution** is the lens through which we look at variation, enabling us to identify and describe variation, and look for and confirm expectations. Distribution is the underlying concept for data representation at all levels of the curriculum.

**Randomness** describes a phenomenon in which the outcome of a single repetition is uncertain, but there is nonetheless a regular distribution of relative frequencies in a large number of repetitions. It is explicitly mentioned in year 8.

**Informal inference** is an evidence-based process balancing the variation and expectation found in sample data when answering a meaningful population-based question. It is implicit throughout the curriculum.