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VCE Further Maths
Chapter Two-Bivariate Data
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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.