What is a Scatter Diagram?
The Scatter diagram method is a simple representation that is popularly used in commerce and statistics to find the correlation between two variables. These two variables are plotted along the X and Y axis on a two-dimensional graph and the pattern represents the association between these given variables. The study of such a graphical representation involving two variables and using such a diagram is known as scatter diagram analysis.
Students must be very particular while plotting such graphs. Scatter diagrams in statistics and commerce are a vital tool that requires precision since their analysis depends on such representations.
Interpretation of Scatter Diagram
Two variables involved in a study are represented on the X and Y axis. These variables can be taken as independent variables, though this makes the second variable dependent on this former one. Correspondingly, all these points are plotted on the graph and their totality is termed as a scatter diagram.
After plotting all these points on a graph, the generated profiles of these scatter plots are used to draw an extrapolation. Consequently, students can also calculate the correlation of coefficient of this given data using their plotted representation. Notably, scatter diagram correlation is a quantitative measure of random variables and their association with each other.
Types of Scatter Diagrams
While understanding its various types, it is important to describe the scatter diagram with examples for a better understanding of the students. Notably, though there can be many representations, each of which suggests different types of correlation, the most common and vital ones are explained below.
Students Should Note the Relevant Graphs Properly
Perfect Positive Correlation: A scatter diagram is known to have a perfect positive correlation if all the plotted points are on a straight line when represented on a graph.
Additionally, students must also note that all these points form a straight line which is rising from its lower-left corner to the top right corner. This can be seen in the representation below.
Perfect Negative Correlation: Among scatter diagram examples, a perfect negative correlation is reciprocal of the previous type. Here, every plotted point lies on a straight line without exception too.
However, unlike in the case of positive correlation, here this plotted point creates a line which is approaching from the top left corner towards the bottom right corner. Students can see its representation in this diagram given below.
High Degree of Positive Correlation: If a scatter diagram represents a high degree of positive correlation then all its plotted points are roughly along a straight line, even though they do not clearly create a line. This representation typically forms a band-like structure which is rising from the bottom left corner towards the top right corner. Typically, these graphs look like the representation below.
High Degree of Negative Correlation: Much like the 2 perfect correlations, high degrees of positive and negative correlation are reciprocal of each other. Representing the scatter diagram meaning and values, in the event of a high degree of negative correlation, every plotted point forms a band that falls from top left corner to the right bottom corner. These graphs look like the one below.
Low Degree of Positive Correlation: Students who have understood these above-mentioned graphs and their representations can easily understand that in the case of a low degree of correlation, be it positive or negative, these plotted points are scattered.
Among the importance of scatter diagrams, a low degree of correlation is also a vital analysis since it suggests incoherence. In a low degree of positive correlation, despite being scattered, these points are found to be slowly rising from its left bottom corner to its top-right corner. The diagrams of such representations look like the below-mentioned representation.
Low Degree of Negative Correlation: Much like the representation immediately above, low degrees of negative correlation are represented on a graph with scatter points. However, despite being scattered, these points have a general tendency of falling from the top left corner of a graph to its bottom right corner. This can be seen in this representation below.
No Correlation: While scattering diagram definition looks to find the correlation between variables, students must note that there can be representations that are incoherent and scattered. This is also a valid analysis since it shows that the 2 given variables are not correlated. In such cases, these plotted points are scattered haphazardly across a graph, like in this representation below.
Much like these various types of scatter diagrams, there are many topics and figures in standard 10 + 2 commerce which are vital for students. Subsequently, Vedantu offers detailed study material accompanied with questionnaires that help students ace their curriculum. Furthermore, Vedantu also offers live classes which are a great option to clear any doubt regarding these chapters.
How to Create a Scatter Diagram?
It's relatively easier to create a scatter diagram using an Excel spreadsheet than making the data table on paper. However, the same steps are followed in both cases.
Let us take a look at the steps to create a scatter diagram:
Record the data in a tabular form either in excel or by hand on paper. The table should have both the variables with their respective values and data range.
Draw a graph showing the independent variable on the x-axis and the dependent variable on the y axis.
Mark a dot on the graph where the values of both the variables intersect.
Observe the pattern, if there is any. If the dots form an obvious line or a curve. It indicates that the variables are correlated.
Divide the graph into four equal quadrants and observe the data points in each quadrant. If there are X points on the graphs, count X/2 points from top to bottom and left to right to make the quadrant.
Count the number of dots that are there in each quadrant.
Find the lesser sum and the total number of dots in the sum of diagonally opposite quadrants.
In such case:
A = dots in upper left + dots in lower right
B = dots in upper right + dots in lower left
Q = the lesser value of A and B
N = A + B
Analyse the table to know the relation between the variables: if Q<N, the variables are related. But, if Q>=N, the pattern is the result of mere chance.
FAQs on Scatter Diagram
1. What are the applications of the Scatter diagram?
Scatter diagrams are used widely in the subjects of commerce and statistics but aren’t limited to only these two subjects. The various applications of scatter graphs or diagrams make it available for use across various fields of study. Let us look at the three major applications of scatter diagram:
Presentation of the relationship between any two variables:
A Scatter diagram essentially represents the distinct relationship between any two variables. This relationship can be either linear or nonlinear, positive or negative, strong or weak. Such representation provides an observation of the two variables which helps in analysing the data through the data points or dots shown in the diagram.
Recognizing the correlational relationship:
There is a correlation between the independent variables present on the horizontal axis and the dependent variables present on the vertical axis. This correlation can be identified and studied by observes to derive a probable value of the dependent variables on the vertical axis. This value is essential for furthering the analysis of different variables.
Observing patterns of data:
Given the various data points or dots, in the scatter diagram the observer can identify the common and uncommon patterns of data, their respective values and the outlier points (abnormal distanced points) present when there are data gaps.
Using the above applications, a scatter diagram helps in identifying the ‘Line of Best Fit’, commonly known as the trendline to observe and interpret various trends across different graphs showing different data.
2. What are the three main types of scatter diagrams?
The three types of scatter diagrams are positive correlation, negative correlation, or no correlation.
3. What type of data is represented in the scatter diagram?
A scatter diagram represents the relationship between two variables that are measured across the same individual.
4. How can one tell if the scatter diagram is negative or positive?
If the data points slant downward from left to right i.e. the value of the variable on the vertical axis decreases as the variable on the horizontal axis increases then the diagram represents a negative relation. And when the data points slant upwards i.e. the value of the variable on the y axis increases as the variable on the x-axis increases then the relationship is positive.
5. What are the common challenges faced in scatter diagrams?
The common challenges faced in scatter diagrams is that of making it and then interpreting it. The two issues are:
Overplotting- Overplotting occurs when there are a lot of overlapping data points which makes it difficult for the observer to analyze the relationship between different variables. When such data points are not scattered but tightly packed it becomes even more difficult to distinguish between different data patterns.
Confusing between correlation and causation- Not only does the making of scatter diagrams can have various challenges but interpreting the graph can also be confusing. It’s common to interpret that related variables are dependent i.e. in case of change in one variable the other variable is bound to change as well. However, it’s not always true. Correlation does not imply causation. It’s very much probable that the visible correlation is caused by a third unseen variable or the pattern observed is merely coincidental.
