VCE Further Mathematics Units 3 and 4 – Data Analysis

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Description

1.1 Descriptive Statistics
1.2 Representing Data
1.3 Exploring Data
1.4 Logarithms
1.5 Normal Distribution
1.6 Time Series




Additional information

Outcome

Data analysis

Key knowledge
• types of data: categorical (nominal and ordinal) and numerical (discrete and continuous)
• frequency tables, bar charts including segmented barcharts, histograms, stem plots, dot plots, and their application in the context of displaying and describing distributions
• log (base 10) scales, and their purpose and application
• five-number summary and boxplots (including the designation and display of possible outliers)
• mean x and standard deviation
• normal model and the 68–95–99.7% rule, and standardised values (z-scores)
• response and explanatory variables
• two-way frequency tables, segmented bar charts, back-to-back stem plots, parallel boxplots, and scatterplots, and their application in the context of identifying and describing associations
• correlation coefficient, r, its interpretation, the issue of correlation and cause and effect
• least squares line and its use in modelling linear associations
• data transformation and its purpose
• time series data and its analysis.

Key skills
• construct frequency tables and bar charts and use them to describe and interpret the distributions of categorical variables
• answer statistical questions that require knowledge of the distribution/s of one or more categorical variables
• construct stem and dot plots, boxplots, histograms and appropriate summary statistics and use them to describe and interpret the distributions of numerical variables
• answer statistical questions that require knowledge of the distribution/s of one or more numerical variables
• solve problems using the z-scores and the 68–95–99.7% rule
• construct two-way tables and use them to identify and describe associations between two categorical variables
• construct parallel boxplots and use them to identify and describe associations between a numerical variable and a categorical variable
• construct scatterplots and use them to identify and describe associations between two numerical variables
• calculate the correlation coefficient, r, and interpret it in the context of the data
• answer statistical questions that require knowledge of the associations between pairs of variables
• determine the equation of the least squares line giving the coefficients correct to a required number of decimal places or significant figures as specified
• distinguish between correlation and causation
• use the least squares line of best fit to model and analyse the linear association between two numerical variables and interpret the model in the context of the association being modelled
• calculate the coefficient of determination and interpret in the context of the association being modelled and use the model to make predictions, being aware of the problem of extrapolation
• construct a residual analysis to test the assumption of linearity and, in the case of clear non-linearity, transform the data to achieve linearity and repeat the modelling process using the transformed data
• identify key qualitative features of a time series plot including trend (using smoothing if necessary), seasonality, irregular fluctuations and outliers, and interpret these in the context of the data
• calculate, interpret and apply seasonal indices
• model linear trends using the least squares line of best fit, interpret the model in the context of the trend being modelled, use the model to make forecasts being aware of the limitations of extending forecasts too far into the future.

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