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VCE Further Maths

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

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

  2. 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.

  3. 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

  4. 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

  5. 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.

  6. 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.

  7. 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.

  8. 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).

  9. 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.

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