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Scatter Diagrams: Data is everything, and it is one of the main reasons it is used to communicate findings in any endeavour. One will need charts or graphs to present data in a simple format, that is where the scatter diagrams come in. A scatter diagram is a tool for analysing relationships between two variables and determining how closely they are related. It is also called a scatter plot, scatter graph, or correlation chart.
It is commonly used to verify cause-and-effect relationships. Although the diagram depicts relationships, it does not prove that one variable causes the other. As a result, we can use a scatter diagram to investigate theories about cause-and-effect relationships and to look for the root causes of a problem.
A scatter plot (also known as an \(x-y\) graph) is a type of chart used to express the relationship between two variables or data points.
Along the \(x\) and \(y-\) axis, two data points are plotted. The independent variable is represented on the \(x-\) axis, while the dependent variable is represented on the \(y-\) axis. When data is plotted, the resulting plot is skewed. You can use scatter plots as a marketer to analyse keyword data in SEM marketing.
Below given are the steps to plot a scatter diagram:
1st Step: To plot the scatter diagram, first record the data in a tabular format, either in Excel or on paper by hand. Both variables, along with their respective values and data ranges, should be included in the table.
2nd Step: Create a graph that shows the independent variable on the \(x\)-axis and the dependent variable on the \(y-\) axis.
3rd Step: Place a dot on the graph where the values of the two variables intersect.
4th Step: If there is a pattern, note it. If the dots form a clear line or curve. It denotes that the variables are linked.
The degree to which the variables are related to one another is determined by how the points are distributed on the chart. The greater the dispersion of the points plotted on the chart, the lower the degree of correlation between the variables.
The higher the degree of correlation, the closer the points plotted are to the line. The degree of correlation is denoted by the letter ” \(r\).” The value of \(r\) lies between \(-1\) and \(1 . r=-1\) states a strong or perfect negative correlation and \(r=+1\) states a strong and positive correlation.
According to the correlation, scatter diagrams can be classified as:
A close examination of the graph reveals that the dots align one line. This arrangement indicates that the data has a strong relationship (or correlation). This is referred to as a scatter diagram with a high correlation.
These diagrams are also known as scatter diagrams with a weak or low degree of correlation, where the data points are somewhat non-linear and drawing a straight line through them is difficult. Also, the data points (shown as dots) are grouped.
In this type of scatter diagram, there is no degree of correlation or alignment. Most of the time, the data points are dispersed all over the place, making it difficult to establish a relationship between them.
A correlation that points in the same direction is referred to as a positive correlation. When one variable increases, the other increases as well, and when one variable decreases, the other decreases as well. The length of an iron bar, for example, will lengthen as the temperature rises.
A negative correlation is a correlation that goes in the opposite direction. If one variable rises, the other falls, and vice versa. For example, as the pressure rises, the volume of gas decreases, and as the price of a commodity falls, the demand for that commodity rises.
The table below indicates the degree of correlation between variable \(X\) and variable \(Y\):
| Correlation Pattern | \(X/Y\) Values |
| Strong Positive Correlation | The value of \(Y\) increases as the value of \(X\) increases. |
| Strong Negative Correlation | The value of \(Y\) decreases as the value of \(X\) increases. |
| Weak Positive Correlation | The value of \(Y\) increases slightly as the value of \(X\) increases. |
| Weak Negative Correlation | The value of \(Y\) decreases slightly as the value of \(X\) increases. |
| Complex Correlation | The value of \(Y\) seems to be related to the value of \(X\), but the relationship is not easy to determine. |
| No Correlation | There is no connection between the two variables. |
Although the diagram depicts relationships, it does not prove that one variable causes the other. As a result, we can use a scatter diagram to investigate theories about cause-and-effect relationships and to look for the root causes of a problem.
We can, for example, examine the pattern of motorcycle accidents on a highway. You draw the diagram after selecting two variables: motorcycle speed and number of accidents. Once the diagram is completed, you will notice that as the speed of the vehicle increases, so does the number of accidents. This demonstrates that there is a link between vehicle speed and accidents on the highway.
A strong positive correlation is said when the correlation coefficient is greater than \(0\) and close to \(+1\). This signifies that both variables move in the same direction and are closely correlated. Since the value is close to \(+1\), the relationship between oil prices and airfares has a very strong positive correlation.
If one of the two variables increases in value while the other decreases, it is said to be a strong negative correlation. A strong negative correlation is there when the value of the correlation coefficient is less than \(0\) and close to \(-1\).
Weak positive correlation is said to have when one variable rises, the other rises as well, but in a weak or unreliable manner.
A weak negative correlation is said to have when one variable rises, the other tends to fall, but only in a weak or unreliable way.
When there is no dependency on the variables, then they are said to be not correlated. No correlation is depicted on a scatter diagram with clustered points without any order.
Q.1. How do the different degrees of correlation plotted on a scatter diagram?
Sol: The different degrees of correlation are perfect correlation, strong or high correlation, weak or low correlation and no correlation. They can be depicted on scatter diagrams as below:
Q.2. Draw a scatter diagram for the given pair of variables and identify the type of correlation between them.
| No. of Students | Marks (out of 100) |
| 12 | 40-50 |
| 10 | 50-60 |
| 8 | 60-70 |
| 7 | 70-80 |
| 5 | 80-90 |
| 2 | 90-100 |
Sol:
The two variables for consideration are:
M: The marks obtained out of 100
S: Numbers 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)
From the diagram, it is understood that only a fewer number of students get high marks. This implies a negative correlation between the two variables.
Q.3. Show the scatter diagram for strong \(+r\), weak \(+r\), strong \(-r\), where \(r\) is the correlation coefficient.
Sol: If the correlation coefficient is strong \(+r\) or \(-r\), it means that all the points will be tightly clustered along the positive or negative slope line. If the correlation coefficient is weak \(+r\) or \(-r\), it means that all the points will be clustered widely along the positive or negative slope line. It can be shown as below:
Q.4. How does a scatter diagram be if there is no correlation between the variables?
Sol: If there is no correlation between the variables, then the dots or points on the scatter diagram will be spread over the graph without any pattern.
Q.5. What are the benefits of scatter diagrams?
Sol: Scatter diagrams are simple to spot. Scatter analysis determines whether there are any real relationships between two variables or data sets. That is, it establishes the connection between two variables. It is the most effective method for displaying a non-linear pattern.
There are multiple values of dependent variables for each independent variable. The data flow range, such as the maximum and minimum value, can be determined. Each variable is represented by a pair of numerical figures that will assist you in determining its value.
A scatter diagram is one of the most effective tools for determining a relationship between two variables. The point of intersection essentially depicts the relationship pattern. The scatter diagram is frequently used to confirm or refute the cause-and-effect relationship between two variables.
The dots on the scatter diagram clustered tightly along the line shows a strong correlation and a loosely or widely clustered dot indicates a weak correlation. When there is no dependency on the variables, then they are said to be not correlated. No correlation is depicted on a scatter diagram with clustered points without any order.
Q.1. What are scatter diagrams used for?
Ans: A scatter diagram’s primary goal is to identify the relationship between two variables. A scatter diagram will be difficult to study data sets with more than two variables. A scatter plot (also known as an x-y graph) is a type of chart used to express the relationship between two variables or data points.
Q.2. What are the 3 types of scatter plots?
Ans: The classification of scatter diagrams is dependent on their correlation and slope type. According to the correlation, scatter diagrams are classified into the following categories:
Q.3. What is a scatter diagram with an example?
Ans: A scatter diagrams, also known as scatter plots, scatter graphs, or correlation chart is a tool for analysing relationships between two variables to determine how closely they are related. One variable is plotted horizontally, while the other is plotted vertically.
Q.4. What are the relationships that can be examined from a scatter plot?
Ans: Many different relationships might be found when examining a scatter plot.
Q.5. What is a scatter diagram with points clustered all around without any pattern mean?
Ans: A scatter diagram with points clustered all around without any pattern means there is no specific correlation between the variables. When there is no dependency on the variables, then they are said to be not correlated. No correlation is depicted on a scatter diagram with clustered points without any order.
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