VCE Further Maths

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VCE Further Maths. Chapter Two-Bivariate Data \\Servernas\Year 12\Staff Year 12\LI Further Maths. Looking at the relationship of two variables. Dependent variable (y) Independent variable (x) In a relationship, the variable that “depend” on the other is referred as the dependent variable.

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### VCE Further Maths

Chapter Two-Bivariate Data

\\Servernas\Year 12\Staff Year 12\LI Further Maths

Looking at the relationship of two variables.
• Dependent variable (y)
• Independent variable (x)
• In a relationship, the variable that “depend” on the other is referred as the dependent variable.
• On a graph, the independent variable on the horizontal axis and the dependent on the vertical axis.
Back-to-back stem plots
• Same process as constructing a single stem plot
• This is used to display relationship between a numerical and a categorical variable with two categories
• Together with summary statistics, back-to-back stem plots can be used for comparing two distributions
Use graphics calculator to generate:
• The mean and the median
• The interquartile range
• The standard deviation
• Commenting on the relationship
• The shape (symmetric or skewed)
• The mean and median (which one is a better measure)
• The interquartile range (the spread)
• Overall comment
Parallel Boxplots
• To display a relationship between a numerical variable and categorical variable with more than two categories.
• Same process as constructing a single boxplot, except that they share a common scale.
• Comparing distributions of a number of boxplots.

The median height increases from Year 9 to Year 11. There is greater variation in 9A’s distribution than in 10A’s. There is a wide range of heights in the lower 25% of the distribution of 9A’s distribution. There is a greater variation in 11A’s distribution than in 10A’s, with a wide range of heights in the top 25% of the 11A distribution.

Two-way frequency tables
• To display the relationship between two categorical variables.
• The figures in the table is expressed as percentages.
• Generally, if the independent variable is placed in the columns of the table, then the percentages should be calculated in columns.
Example: In a survey, 139 women and 102 men were asked whether they approved or disapproved of a proposed freeway. Thirty-seven women and 79 men approved of the freeway. Display these data in a two-way table (not as percentages).
Segmented bar charts
• Segmented bar charts are also useful to display relationship between two categorical variables.
• Same process as discussed in chapter One, where figures are converted in percentages.