MAKING A SCATTER PLOT
We know that a set of bivariate data involves two variables. Bivariate data can be used to explore the relationship between two variables. We can graph bivariate data on a scatter plot. A scatter plot is a graph with points plotted to show the relationship between two variables or two sets of data.
Example :
The final question on a science test reads, how many hours we spent studying for this test. The teacher records the number of hours each student studied and the marks scored by the respective student on the test.
Hours Spent for Studying
0
0.5
1
1
1.5
1.5
2
3
4
Marks Scored by the Students
75
80
80
85
85
95
90
100
90
Step 1 :
Make a prediction about the relationship between the number of hours spent studying and marks scored.
When we look at the above data, we can make the following prediction. A greater number of study hours are likely to be associated with higher marks.
Step 2 :
Make a scatter plot. Graph hours spent studying as the independent variable and marks scored by the students as the dependent variable.
Moreover, if we consider hours spent for studying as variable "x" and marks scored by the students as variable "y", we can write the above data as ordered pairs in the form (x, y).
Then, we have
(0, 75), (0.5, 80), (1, 80), (1, 85), (1.5, 85), (1.5, 95), (2, 90), (3, 100) and (4, 90).
Plot these points on a graph paper.
Reflect
1. What trend can we see in the data ?
In general, when students increase the number of study hours, the marks scored by them are also getting increased.
2. Can we conclude the grade associated with studying for 10 hours would follow this trend ?
No
The graph shows a general upward trend, but the marks scored by the students cannot exceed 100.
3. Can we say this relationship as positive or negative ?
Positive
Because, when one variable (x) is increased, the other variable (y) is also getting increased.
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