Scatter plot is a mathematical technique that is used to represent data. Scatter plot also called a Scatter Graph, or Scatter Chart uses dots to describe two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point.
In this article, we have covered the definition of a Scatter Plot, Scatter Plot Graph, How to Construct a Scatter Plot, and others in detail.
What is a Scatter Plot?
Scatter plot is one of the most important data visualization techniques and it is considered one of the Seven Basic Tools of Quality. A scatter plot is used to plot the relationship between two variables, on a two-dimensional graph that is known as Cartesian Plane on mathematical grounds.
It is generally used to plot the relationship between one independent variable and one dependent variable, where an independent variable is plotted on the x-axis and a dependent variable is plotted on the y-axis so that you can visualize the effect of the independent variable on the dependent variable. These plots are known as Scatter Plot Graph or Scatter Diagram.
Applications of Scatter Plot
As already mentioned, a scatter plot is a very useful data visualization technique. A few applications of Scatter Plots are listed below.
- Correlation Analysis: Scatter plot is useful in the investigation of the correlation between two different variables. It can be used to find out whether two variables have a positive correlation, negative correlation or no correlation.
- Outlier Detection: Outliers are data points, which are different from the rest of the data set. A Scatter Plot is used to bring out these outliers on the surface.
- Cluster Identification: In some cases, scatter plots can help identify clusters or groups within the data.
Scatter Plot Graph
Scatter Plot is known by several other names, a few of them are scatter chart, scattergram, scatter plot, and XY graph. A scatter plot is used to visualize a data pair, such that each element gets its axis, generally the independent one gets the x-axis and the dependent one gets the y-axis.
This kind of distribution makes it easier to visualize the kind of relationship, the plotted pair of data is holding. So Scatter Plot is useful in situations when we have to find out the relationship between two sets of data, or in cases when we suspect that there may be some relationship between two variables and this relationship may be the root cause of some problem.
Now let us understand how to construct a scatter plot and its use case via an example.
How to Construct a Scatter Plot?
To construct a scatter plot, we have to follow the given steps.
Step 1: Identify the independent and dependent variables
Step 2: Plot the independent variable on x-axis
Step 3: Plot the dependent variable on y-axis
Step 4: Extract the meaningful relationship between the given variables.
Let's understand the process through an example. In the following table, a data set of two variables is given.
Matches Played
|
2
|
5
|
7
|
1
|
12
|
15
|
18
|
|---|
Goals Scored
|
1
|
4
|
5
|
2
|
7
|
12
|
11
|
|---|
Now in this data set there are two variables, first is the number of matches played by a certain player and second is the number of goals scored by that player. Suppose, we aim to find out the relationship between the number of matches played by a certain player and the number of goals scored by him/her. For now, let us discard our obvious intuitive understanding that the number of goals scored is directly proportional to the number of matches played. For now, let us assume that we just have the given dataset and we have to extract out relationship between given data pair.
As you can see in the given Scatter Plot, there is some kind of relationship between number of matches played and number of goals scored by a certain player.
Types of Scatter Plot
On the basis of correlation of two variables, Scatter Plot can be classified into following types.
- Scatter Plot For Positive Correlation
- Scatter Plot For Negative Correlation
- Scatter Plot For Null Correlation
Scatter Plot For Positive Correlation
In this type of scatter-plot, value on y-axis increases on moving left to right. In more technical terms, if one variable is directly proportional to another, then, the scatter plot will show positive correlation. Positive correlation can be further classified into Perfect Positive, High Positive and Low Positive.
Scatter Plot For Negative Correlation
In this type of scatter-plot, value on the y-axis decreases on moving left to right. In other words, the value of one variable is decreasing with respect to the other. Positive correlation can be further classified into Perfect Negative, High Negative and Low Negative.
Scatter Plot For Null Correlation
In this type of scatter-plot, values are scattered all over the graph. Generally this kind of graph represents that there is no relationship between the two variables plotted on the Scatter Plot.
What is Scatter Plot Analysis?
Scatter plot analysis involves examining the distribution of the points and interpreting the overall pattern to gain insights into the relationship between the variables. Scatter Plot is used to visualise the relationship between two variables, but in real life, situations are not so ideal that we get only correlated variables. In real life there are situations, when more than two variables are correlated with each other.
In such situations, we do use the Scatter Plot Matrix. For n number of variables, scatter plot matrix will have n rows and n columns where scatter plot of variables xi and xj will be located at ith row and jth column.
Check:
Solved Examples on Scatter Plot
Example 1: Draw a scatter plot for the given data that shows the number of IPL matches played and runs scored in each instance.
Matches Played
|
10
|
12
|
14
|
16
|
18
|
|---|
Runs Scored
|
287
|
300
|
297
|
350
|
345
|
|---|
Solution:
X-axis: Number of Matches Played
Y-axis: Number of Runs Scored
Graph:
Example 2: Prices (in dollars) and the ratings (out of 5 stars) of 5 different restaurants are recorded and plotted on a scatter plot. Interpret the scatter plot to determine if there is any relationship between price and rating.
Resturant
| A
| B
| C
| D
| E
|
|---|
Prices (in dollars)
|
22
|
29
|
15
|
18
|
23
|
|---|
Ratings (out of 5 stars)
|
3.5
|
4.0
|
3.0
|
4.0
|
3.5
|
|---|
Solution:
Graph:
Practice Questions on Scatter Plot
Q1. Draw a scatter plot for the given data that shows the number of T-20 World Cup matches played and wicket taken in each instance.
Matches Played
|
6
|
7
|
8
|
9
|
10
|
|---|
Wicket
|
9
|
9
|
12
|
15
|
16
|
|---|
Q2. Heights (in cm) and weights (in kg) of five individuals are recorded and plotted on a scatter plot. Describe the relationship between height and weight based on the scatter plot.
Individuals
| A
| B
| C
| D
| E
|
|---|
Height(in cm)
|
167
|
179
|
181
|
172
|
159
|
|---|
Wight (in kg)
|
77
|
89
|
79
|
75
|
83
|
|---|
Q3. A student records the number of hours spent studying and the score obtained on a test for 5 subjects. Create a scatter plot showing the relationship between study hours and test scores.
Subjects
| Mathematics
| Physics
| Chemistry
| Computers
| English
|
|---|
Hours Stuied
|
8
|
6
|
11
|
9
|
16
|
|---|
Marks out of 50
|
35
|
33
|
45
|
39
|
48
|
|---|
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