Data Analysis

Data analysis | NSW Curriculum Website

MST-11-08 displays and analyses datasets using summary statistics and graphical representations

📖 Prior Knowledge

Content	Prior knowledge	Used for
Data Classification and Visualisation	- classifying data - creating and interpreting graphs	- repeated content - grouped data
Data Analysis	- surveys and samples - summary statistics	- repeated content - calculating summary statistics from grouped data
Data Analysis A	- standard deviation - box plots	- repeated content - formal definition of an outlier

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
Calculate the range and population standard deviation of a dataset using a scientific calculator or other digital tools
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
Apply $Q_{1} - 1.5 \times I QR$ and $Q_{3} + 1.5 \times I QR$ to formally identify outliers
Explain the impact of outliers on the measures of centre and spread