BIVARIATED DATA

1
BIVARIATED DATA

• In Bivariated Data we investigate the
  relationship between two variables.

One of the variables is classified Independent
Variable (IV) and is the variable that does the
influencing.
The other variable is the Dependent Variable (
DV) and is the variable that has been influenced.
2
Example 1 Classify the following variables as
Independent and Dependent.

• a. The Amount of alcohol consumed and Reaction
  time.
• Answer
• The Amount of alcohol is the Independent
  Variable.
• The Reaction time is the Dependent Variable.
• b. The Hours employed per week and Salary.
• Answer
• The Hours employed per week is the Independent
  Variable.
• The Salary is the Dependent Variable.

3
INVESTIGATING THE RELATIONSHIP BETWEEN TWO
CATEGORICAL VARIABLES

• To investigate the relationship between two
  Categorical Variables, we organise them in a Two
  Way Frequency Table.
• In addition we display them in a Segmented- Bar
  Chart.
• For the Segmented- Bar Chart the Frequency is
  always converted to Percentage Frequency.
• The Independent Variable is always placed
  horizontally and the Dependent Variable
  vertically.

4
Example Organise and display the Attitude
to gun control of 100 people who 62 voted For
and out of them 32 were Males. The total number
of Females were 42.Write a report of your
observations.

• Answer
• a. Classify the data as IV and DV.
• The gender is Independent variable and the
  attitude is the dependent.
• b. Organise them on a frequency table and find
  the values that are missing and the percentage
  frequency.

5

• Frequency table

Attitude Gender
Male Percentage Female Percentage Total
For 32 32100 58 55.2 30 71.4 62
Against 26 44.8 12 28.6 38
Total 58 100 42 100 100
6
c. Construct the Segmented Bar Chart using the
information from the frequency table

• Segmented Bar Chart
• Percentage Frequency
• 100
  for
• 80
  against
• 60
• 40
• 20
• 0
• male female
  gender
  
  
• 
  
• 
  

7
Report From the Frequency table and the
Segmented- Bar Chart we conclude that a higher
Percentage of Females supported gun control than
males, 71.4 to 55.2. This indicates that a
persons attitude to gun control is related to
the gender.

• Example a Fill in the entries that are missing
  in the following table
• 
  Year group

Level of internet usage 3 -6 7-10 11-12 Total
Never used 44 9 8
Sometimes used 16 58
Often used 10 47
Total 73 217
8
Answer3-6, total 70Never used total
61Often used total 98Sometimes used,
11-12 18Sometimes used, 7-10 24Often
used, 7-10 417-10, total 74

• Example b Convert the above Two- Way Frequency
  table to a Percentage- Frequency Table and
  construct a Segmented Bar Chart.

9
INVESTIGATING THE RELATIONSHIP BETWEEN A
CATEGORICAL AND A NUMERICAL VARIABLE

• To investigate the relationship between a
  Numerical and a Categorical Variable
• with two categories, we use
• Back- to- Back Stem and Leaf Plots.
• To investigate the relationship between a
  Numerical and a Categorical Variable
• with more than two categories we use Parallel
  Box Plots.

10
Example 1 The following Stem and Leaf Plot
displays the Travel times in minutes of
destinations A and B.a. Compare and interpret
the destinations in terms of centre,mode and
shape.b. What is the percentage of travel times,
either route, that were more than 60 minutes?

Travel times route A stem Travel times route B
8 5 3 2 2 6 9
9 6 6 4 1 1 0 3 0 3 4 6 8
4 2 2 0 0 4 0 1 2 5 9 9
0 5 1 1 4 7
1 0 6
7 1
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Answer a. The shape of the distribution of
route A is positively skewed since most (mode)
of the travel times are in 30s and it tails to
the right. The shape of the distribution of
route B is symmetric since most of the travel
times are in the middle of the distribution. The
Median of route A is 36 minutes, whereas the
Median of route B is 41.5, indicating that it
takes longer to travel route B.

• b. Percentage of more than 60 minutes 2 100
  5
• 
  37
• 
  

12
Example 2 The parallel box plots below show the
rare of growth of trees of these three samples.
What is the rate of growth and variability of the
trees in cold conditions compared to hot and
mild?

• 
  hot conditions
• 
  
  mild conditions
• 
  
  cold conditions
• rate of growth (in
  centimetres per year)

13

• Answer
• The rate of growth in cold conditions is higher
  since the median is higher. The variability of
  the trees in cold conditions is smaller, because
  the range and IQR is smaller.