This is Chapter 11 – Statistics for the Year 11 Mathematical Methods course.

This chapter shifts the focus from exact algebraic relationships to the analysis of real data. Students learn how statistical measures can summarise a data set while also recognising that no single number can describe every important feature of a distribution.

We begin with key statistical concepts such as populations, samples, variables and different forms of data. Students consider how data is collected and organised before using measures of centre to describe a typical value within a distribution.

Measures of spread then describe how variable the observations are around that centre. Range and related summaries provide an initial picture, while variance and standard deviation introduce more formal measures that become increasingly important in Year 12 statistics. Graphical summaries and the shape of a distribution are considered alongside numerical measures so that students develop a more complete picture of centre, spread and unusual observations.

Students are expected not only to calculate statistical values but also to interpret them. Two data sets can have similar centres but very different spreads, so conclusions should compare both features and remain connected to the context. Calculator use is important, but the explanation attached to the output is equally significant.

The normal distribution provides an important model for data that cluster around a central value in a symmetric pattern. Statistical reasoning is used throughout medicine, psychology, economics, sport science and data analytics and forms the foundation for probability distributions and inference in Stage 2.

Subchapters:

• 11A: Key statistical concepts
  
• 11B: Measuring the centre of data
• 11C: Measuring the spread of data
• 11D: Variance and standard deviation
• 11E: The normal distribution

By the end of this chapter, students will be able to summarise and compare data using measures of centre and spread and interpret the normal distribution with clear statistical reasoning.