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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

VCE Further Maths

Chapter Two-Bivariate Data

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

slide2
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.
slide3
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
slide4
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
slide5
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.
slide6

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
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.
slide8
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
  • 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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