Scatter Diagrams are convenient mathematical tools to study the correlation between two random variables.
The Scatter Diagrams between two random variables feature the variables as their x and y-axes. We can take any variable as the independent variable in such a case (the other variable being the dependent one), and correspondingly plot every data point on the graph (xi,yi ). The totality of all the plotted points forms the scatter diagram.
Based on the different shapes the scatter plot may assume, we can draw different inferences. We can calculate a coefficient of correlation for the given data. It is a quantitative measure of the association of the random variables. Its value is always less than 1, and it may be positive or negative.
In the case of a positive correlation, the plotted points are distributed from lower left corner to upper right corner (in the general pattern of being evenly spread about a straight line with a positive slope), and in the case of a negative correlation, the plotted points are spread out about a straight line of a negative slope) from upper left to lower right.
If the points are randomly distributed in space, or almost equally distributed at every location without depicting any particular pattern, it is the case of a very small correlation, tending to 0.
Draw the scatter diagram for the given pair of variables and understand the type of correlation between them.
| No. of Students |
Marks obtained (out of 100) |
| |
|
| 12 |
40-50 |
| 10 |
50-60 |
| 8 |
60-70 |
| 7 |
70-80 |
| 5 |
80-90 |
| 2 |
90-100 |
Solution:
Here, we take the two variables for consideration as:
M: The marks obtained out of 100
S: Number of students
Since the values of M is in the form of bins, we can use the centre point of each class in the scatter diagram instead. So let us first choose the axes of our diagram.
X-axis – Marks obtained out of 100
Y-axis – Number of Students
The data points that we need to plot according to the given dataset are –
(45,12), (55,10), (65,8), (75,7), (85,5), (95,2)
Here’s how the plot will look like –
From the shape of the curve, clearly, only a fewer number of students get high marks. This implies a negative correlation between the two variables.
Test
Gaurav Seth 6 years, 9 months ago
Scatter Diagrams are convenient mathematical tools to study the correlation between two random variables.
The Scatter Diagrams between two random variables feature the variables as their x and y-axes. We can take any variable as the independent variable in such a case (the other variable being the dependent one), and correspondingly plot every data point on the graph (xi,yi ). The totality of all the plotted points forms the scatter diagram.
Based on the different shapes the scatter plot may assume, we can draw different inferences. We can calculate a coefficient of correlation for the given data. It is a quantitative measure of the association of the random variables. Its value is always less than 1, and it may be positive or negative.
In the case of a positive correlation, the plotted points are distributed from lower left corner to upper right corner (in the general pattern of being evenly spread about a straight line with a positive slope), and in the case of a negative correlation, the plotted points are spread out about a straight line of a negative slope) from upper left to lower right.
If the points are randomly distributed in space, or almost equally distributed at every location without depicting any particular pattern, it is the case of a very small correlation, tending to 0.
Draw the scatter diagram for the given pair of variables and understand the type of correlation between them.
Solution:
Here, we take the two variables for consideration as:
M: The marks obtained out of 100
S: Number of students
Since the values of M is in the form of bins, we can use the centre point of each class in the scatter diagram instead. So let us first choose the axes of our diagram.
X-axis – Marks obtained out of 100
Y-axis – Number of Students
The data points that we need to plot according to the given dataset are –
(45,12), (55,10), (65,8), (75,7), (85,5), (95,2)
Here’s how the plot will look like –
From the shape of the curve, clearly, only a fewer number of students get high marks. This implies a negative correlation between the two variables.
2Thank You