VCE Further Maths Chapter Two-Bivariate Data \\Servernas\Year 12\Staff Year 12\LI Further Maths

Looking at the relationship of two variables. Looking at the relationship of two variables. Dependent variable (y) Dependent variable (y) Independent variable (x) Independent variable (x) In a relationship, the variable that “depend” on the other is referred as the dependent variable. 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. On a graph, the independent variable on the horizontal axis and the dependent on the vertical axis.

Back-to-back stem plots 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: Use graphics calculator to generate: –The mean and the median –The interquartile range –The standard deviation Commenting on the relationship 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 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. To display the relationship between two categorical variables. The figures in the table is expressed as percentages. 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. 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).AttitudeWomenMenTotal Approved Disapproved Total AttitudeWomenMenTotalApproved32%68%100% Disapproved82%18%100% AttitudeWomenMenApproved27%77% Disapproved73%23% Total100%100%

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