vce further maths chapter two-bivariate data \\servernas\year 12\staff year 12\li further maths
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VCE Further Maths VCE Further Maths
Chapter Two-Bivariate DataChapter Two-Bivariate Data
\\Servernas\Year 12\Staff Year 12\\\Servernas\Year 12\Staff Year 12\LI Further MathsLI Further Maths
• Looking at the relationship of two Looking at the relationship of two variables.variables.
• Dependent variable (y)Dependent variable (y)
• Independent variable (x)Independent variable (x)
• In a relationship, the variable that In a relationship, the variable that “depend” on the other is referred as “depend” on the other is referred as the dependent variable.the dependent variable.
• On a graph, the independent variable On a graph, the independent variable on the horizontal axis and the on the horizontal axis and the dependent on the vertical axis.dependent on the vertical axis.
• Back-to-back stem plotsBack-to-back stem plots– Same process as constructing a single Same process as constructing a single
stem plotstem plot– This is used to display relationship This is used to display relationship
between a numerical and a categorical between a numerical and a categorical variable with two categoriesvariable with two categories
– Together with summary statistics, back-Together with summary statistics, back-to-back stem plots can be used for to-back stem plots can be used for comparing two distributionscomparing two distributions
• Use graphics calculator to generate:Use graphics calculator to generate:– The mean and the medianThe mean and the median– The interquartile rangeThe interquartile range– The standard deviationThe standard deviation
• Commenting on the relationshipCommenting on the relationship– The shape (symmetric or skewed)The shape (symmetric or skewed)– The mean and median (which one is a The mean and median (which one is a
better measure)better measure)– The interquartile range (the spread)The interquartile range (the spread)– Overall commentOverall comment
• Parallel BoxplotsParallel Boxplots– To display a relationship between a To display a relationship between a
numerical variable and categorical numerical variable and categorical variable with variable with more more than two categories.than two categories.
– Same process as constructing a single Same process as constructing a single boxplot, except that they share a boxplot, except that they share a common scale.common scale.
– Comparing distributions of a number of Comparing distributions of a number of boxplots.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 tablesTwo-way frequency tables
• To display the relationship between To display the relationship between two categorical variables.two categorical variables.
• The figures in the table is expressed The figures in the table is expressed as percentages.as percentages.
• Generally, if the independent Generally, if the independent variable is placed in the columns of variable is placed in the columns of the table, then the percentages the table, then the percentages should be calculated in columns.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).
AttitudeAttitude WomeWomenn
MenMen TotalTotal
ApprovedApproved 3737 7979 116116
DisapprovDisapproveded
102102 2323 125125
TotalTotal 139139 102102 241241
AttitudeAttitude WomenWomen MenMen TotalTotal
ApprovedApproved 32%32% 68%68% 100%100%
DisapprovDisapproveded
82%82% 18%18% 100%100%
AttitudeAttitude WomenWomen MenMen
ApprovedApproved 27%27% 77%77%
DisapproveDisapprovedd
73%73% 23%23%
TotalTotal 100%100% 100100%%
Segmented bar chartsSegmented bar charts
• Segmented bar charts are also useful Segmented bar charts are also useful to display relationship between two to display relationship between two categorical variables.categorical variables.
• Same process as discussed in Same process as discussed in chapter One, where figures are chapter One, where figures are converted in percentages.converted in percentages.