Transcript Chap 2 Biv
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-toback 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). Attitude Women Men Total Approved 37 79 116 Disapproved 102 23 125 Total 139 102 241 Attitude Women Men Total Approved 32% 68% 100% Disapproved 82% 18% 100% Attitude Women Men Approved 27% 77% Disapproved 73% 23% Total 100% 100% 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.