11–12Mathematics Standard 11–12 Syllabus

Identify an issue and pose a question to a targeted population to gather statistical information

Develop a survey by applying questionnaire design principles of clear language, unambiguous questions and consideration of number of choices

Examine issues of privacy, bias, ethics and responsiveness to diverse groups and cultures

Compare and contrast systematic sampling, self-selected sampling, random sampling and stratified sampling

Justify whether a sample obtained from a population is representative of the population by considering the sampling method

Describe the potential faults in the design and practicalities of a data collection process by considering survey design, experiments and observational studies, and misunderstandings and misrepresentations

Classify and describe variables as numerical or categorical

Describe a numerical variable as discrete or continuous

Describe a categorical variable as nominal or ordinal

Identify collections of data that can be described as numerical or categorical depending on responses

Recognise and explain why some datasets need to be grouped to allow for appropriate representation and analysis

Use a spreadsheet to organise and represent data using appropriate graphs

Represent a numerical dataset as either a frequency distribution table or a cumulative frequency distribution table and graph the associated histogram with polygon, both with and without using digital tools

Represent categorical datasets in tables and column graphs as appropriate, with and without using digital tools

Select the type of graph best suited to represent various single datasets and justify the choice of graph

Identify and describe the shape of the distribution of a dataset as either symmetric, positively skewed or negatively skewed

Interpret and analyse dot plots, line graphs, sector graphs, stem-and-leaf plots, back-to-back stem-and-leaf plots and divided bar charts related to real-world applications

Analyse a statistical infographic and justify the choice of graphical representations used for the relevant dataset

Interpret and consider limitations of graphical representations to make conclusions and predictions

Explain why a given graphical representation can lead to a misinterpretation of data

Describe the mean, median and mode as measures of centre and calculate their values for a dataset in graphical form and tabular form, using a scientific calculator and other digital tools

Identify and describe datasets as uniform, unimodal, bimodal or multimodal

Identify the range and standard deviation as measures of spread to describe variation in a dataset

Compare datasets using measures of centre and measures of spread

Examine the merits of each measure of centre and justify where each measure is most appropriately used

Identify and describe real-world examples illustrating appropriate and inappropriate uses of measures of centre and measures of spread

Use a spreadsheet to analyse data including calculating measures of centre and spread

Determine the five-number summary from a set of numerical data or graphical representation

Determine the interquartile range (IQR) of datasets

Compare and contrast the use of range and IQR as measures of spread

Represent numerical datasets using a box plot to display a five-number summary, with and without using digital tools

Compare and contrast the measures of centre, spread and shape using parallel box plots

Determine quartiles from datasets displayed in histograms and dot plots, and represent these datasets as a box plot

Interpret box plots to draw conclusions and make inferences about a dataset

Identify clusters, gaps and outliers and explain their occurrence in the context of the data

Explain the impact of outliers on the measures of centre and spread