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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.
- 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.

- 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 are also useful to display relationship between two categorical variables.
- Same process as discussed in chapter One, where figures are converted in percentages.