Nature Through Maths

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Curriculum Audit

• VCE Unit 3
  • VCE - Further Mathematics
    • Area of Study 1
      • Data analysis
        • review of types of data
        • review of representation, display and description of the distributions of categorical variables: data tables, two-way frequency tables and their associated segmented bar charts
        • use of the distribution/s of one or more categorical variables to answer statistical questions
        • review of representation, display and description of the distributions of numerical variables: dot plots, stem plots, histograms; the use of a log (base 10) scale to display data ranging over several orders of magnitude and their interpretation in powers of ten
        • summary of the distributions of numerical variables; the five-number summary and boxplots (including the use of the lower fence (Q1 - 1.5 × IQR) and upper fence (Q3 + 1.5 × IQR) to identify and display possible outliers); the sample mean and standard deviation and their use in comparing data distributions in terms of centre and spread
        • use of the distribution/s of one or more numerical variables to answer statistical questions
        • the normal model for bell-shaped distributions and the use of the 68-95-99.7% rule to estimate percentages and to give meaning to the standard deviation; standardised values (z-scores) and their use in comparing data values across distributions
        • response and explanatory variables and their role in investigating associations between variables
        • contingency (two-way) frequency tables, two-way frequency tables and their associated bar charts (including percentaged segmented bar charts) and their use in identifying and describing associations between two categorical variables
        • back-to-back stem plots, parallel dot plots and boxplots and their use in identifying and describing associations between a numerical and a categorical variable
        • scatterplots and their use in identifying and qualitatively describing the association between two numerical variables in terms of direction (positive/negative), form (linear/non-linear) and strength strong/moderate/weak)
        • answering statistical questions that require a knowledge of the associations between pairs of variables
        • Pearson correlation coefficient, r, its calculation and interpretation
        • cause and effect; the difference between observation and experimentation when collecting data and the need for experimentation to definitively determine cause and effect
        • non-causal explanations for an observed association including common response, confounding, and coincidence; discussion and communication of these explanations in a particular situation in a systematic and concise manner
        • least squares line of best fit y = a + bx, where x represents the explanatory variable and y represents the response variable; the determination of the coefficients a and b using technology, and the formulas
        • modelling linear association between two numerical variables
        • identification of the explanatory and response variables
        • use of the least squares method to fit a linear model to the data
        • interpretation of the slope and intercepts of the least squares line in the context of the situation being modelled
        • use of the rule of the fitted line to make predictions being aware of the limitations of extrapolation
        • use of the coefficient of determination, r^2, to assess the strength of the association in terms of explained variation
        • use of residual analysis to check quality of fit
        • interpretation and use of the equation of the least squares line fitted to the transformed data to make predictions

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