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: Meaning and Uses
1. What is a scatter diagram in Statistics?
A scatter diagram, also known as a scatter plot or scatter graph, is a mathematical diagram that uses Cartesian coordinates to display values for two different variables for a set of data. Each point on the graph represents a pair of values, one for each variable, helping to visually show if there is a relationship or correlation between them. It is a fundamental tool used in statistics to analyze trends and patterns.
2. What types of correlation can a scatter diagram illustrate?
A scatter diagram can illustrate three main types of correlation between two variables:
- Positive Correlation: When the values of both variables tend to increase together. The points on the diagram generally rise from left to right.
- Negative Correlation: When the value of one variable increases as the value of the other variable decreases. The points on the diagram generally fall from left to right.
- No Correlation: When there is no clear pattern or relationship between the two variables. The points appear scattered randomly across the graph.
3. How are scatter diagrams applied in real-world situations?
Scatter diagrams have wide-ranging applications in various fields such as economics, business, science, and social studies. They are used to:
- Identify Relationships: For instance, studying the relationship between advertising expenditure and sales revenue.
- Recognize Trends: Observing how changes in one variable, like temperature, might affect another, such as ice cream sales.
- Detect Outliers: Spotting unusual data points that deviate significantly from the general pattern, which might indicate anomalies or errors.
- Support Decision Making: Providing a visual basis for understanding how variables interact, aiding in predictions and strategic planning.
4. What kind of data is suitable for representation on a scatter diagram?
Scatter diagrams are specifically designed for visualizing bivariate data, which means data that involves two quantitative variables. Both variables should be measurable and associated with the same individual or observation. For example, you can use a scatter diagram to plot a student's marks in two different subjects, or a city's pollution levels against the number of respiratory illnesses.
5. What are the common challenges when interpreting a scatter diagram?
While scatter diagrams are useful, they come with certain interpretation challenges:
- Overplotting: When many data points overlap, especially in dense areas, it can obscure the true relationship or patterns, making it hard to distinguish individual points.
- Confusing Correlation with Causation: A crucial challenge is mistaking correlation for causation. A scatter diagram only shows if two variables move together, not if one directly causes the other. A third, unobserved variable might be the actual cause, or the observed correlation could be purely coincidental.
- Identifying Non-linear Relationships: Scatter diagrams are excellent for linear relationships, but interpreting complex non-linear patterns can be difficult without additional statistical analysis.
6. Why is drawing a 'Line of Best Fit' important for understanding scatter diagram data?
The Line of Best Fit (or trendline) is a straight line drawn through the middle of the data points on a scatter diagram, representing the general trend. It's important because it helps to:
- Summarize the Relationship: It provides a clear visual summary of the overall direction and strength of the relationship between the two variables.
- Make Predictions: Once established, this line can be used to estimate or predict the value of one variable based on the value of the other, even for data points not originally plotted.
- Quantify Correlation: Its slope and position help statisticians determine the mathematical relationship between the variables more precisely, often leading to the calculation of correlation coefficients.
7. How do strong and weak correlations appear differently on a scatter diagram?
The appearance of points on a scatter diagram helps distinguish between strong and weak correlations:
- A strong correlation is indicated when the data points are tightly clustered closely around the line of best fit, forming a distinct upward or downward trend. This suggests a highly predictable relationship where changes in one variable are consistently associated with changes in the other.
- A weak correlation is visible when the data points are widely dispersed and do not form a clear line or trend. While some relationship might exist, it is inconsistent and less predictable, meaning the variables are not closely associated.
8. Can a scatter diagram indicate the direction of a relationship without showing its strength?
No, a scatter diagram is designed to show both the direction and the strength of the relationship between two variables simultaneously. The direction (positive, negative, or no correlation) is observed by the overall trend of the points (upward, downward, or scattered). The strength is indicated by how tightly the points cluster together; the closer they are to forming a straight line, the stronger the relationship. It provides a complete visual overview of the bivariate relationship.
