Scatter plot is a graph of plotted points that show the relationship between two sets of data where they are similar to line graphs, in that they use horizontal and vertical axes to plot data points. Through Scatter plots one can determine how much one variable is affected by another. The relationship between two variables is called their correlation. A scatter plot is a plot of the values of Y versus the corresponding values of X.

Scatter plot very clearly helps us to identify the association between two variables, which is explanatory variable and response variable. If we want to show the relationship between two given sets then we can use the scatter plot. We can create the scatter plot by using ordered pairs of given sets in a Cartesian coordinate system. This is a way to show the correlation between bivariate data. In this plot, first variable lies on x-axis(horizontal axis) and the second variable lies on y-axis(vertical axis).
If the data points make a straight line going from the origin out to high x and y-values, then the variables are said to be positively correlated. If the line goes from a high-value on the y-axis down to a high-value on the x-axis then the variables are negatively correlated. Perfect positive and perfect negative correlation lies in the range of (-1, +1). If the value is Zero then we say there is no correlation among the variables.

Strong Negative CorrelationsStrong Positive CorrelationWeak Negative Correlation
Strong Negative CorrelationModerate Negative CorrelationNo Correlation


Given below is the table which helps you in understanding the relationship between two variables and their association.

Less than 0.2
Very weak relationship
0.2-0.4 Weak Relationship
0.4-0.6 Moderate Relationship
0.6-0.8 Strong Relationship
Greater than 0.8 Very strong Relationship

If there is no relation between the sets A and B, then scatter graph shows no trend.

To know about the trend, we draw the line of best fit. If the slope of the line is positive then we say there is a positive trend between the sets and if the slope of the line is negative then the trend is said to be negative.

Solved Examples

Question 1: Consider  the ranking of eight tennis players along with their practice time(min) as shown below
                   
Practice Time( Min)
 Ranking
 150  1
 300  6
 100  3
 90  5
 250  7
 320  2
 180  8
 110  4

Solution:
 
Taking practising time(min) on the x-axis and ranking of the players on y-axis we get the following scatter plot for the given set of bivariate data, which shows that there is no trend between the given sets of ordered pairs.
             Scatter Plot Example
 

Question 2: Ohm's law is an important relationship in the area of physics. Below is a table between the current and voltage. Make a scatter plot for this data.

 Current   Voltage
1.0  0.4
2.1  0.3
3.0  0.6
4.0  0.6
5.0  0.4
6.0  1.0
7.0  0.9
8.0  0.7
9.0  1.0
10.0  1.1
 11.0  1.3
12.0  1.1
13.0  1.4
14.0  1.6

Solution:
 
The gradient of the graph is known as the resistance of the conductor. In this Cartesian coordinate system, current is on x-axis and voltage is on y-axis.From the below graph we see that there is positive correlation between current and voltage.
Scatter Plot Example Problem
 


Solved Examples

Question 1: The local ice cream shop keeps track of how much ice cream they sell versus the temperature on that day. Here are their figures for the last 15 days:
Temperature
Sales
 19.0  $270
 25.4  $440
16.0  $480
 17.0  $258
 26  $260
 27.0  $245
 32.0  $275
 25.0  $162
 17.0  $593
 19.0  $215
 18.0  $593
 19.0  $324
 28.0 $270
 17.0  $408
 16.0  $215

(1) Construct a scatter plot for the data.
(2) What kind of correlation is present in the data?
Solution:
 

Scatter Plot Word Problem

From the above figure we see that there is no correlation between Ice cream sales and temperature for the given problem.
 

Question 2: Given below are the prices of diesel and milk at a local convenience store for a period of three weeks.
Examine this data for correlations between the price of diesel and the price of milk. Comment on the correlation
Diesel 
Milk
 2.89  2.35
 2.95  2.40
 3.04  2.43

Solution:
 

Scatter Plot Word Problems
Here we see that there is strong positive correlation between price of diesel and price of milk.