Introduction
Scatter plots are a powerful tool used to visualize relationships between two variables. In this article, we will explore different types of scatter plots and what they can tell us about correlation and association.
No Correlation Graph: (35, 50), (50, 35), and (70, 50)
One type of scatter plot is the no correlation graph, where there is no pattern or relationship between the variables. This type of graph is characterized by a random distribution of data points with no linear or non-linear relationship.
Example: A student collects data on their classmates' foot size (measured from heel to longest toe) and arm length (measured from shoulder to wrist), both measured in inches.
| x | y |
|---|---|
| 8 | 12 |
| 7 | 13 |
| 6.5 | 12.5 |
| 7 | 15 |
| 6 | 10 |
| 7.5 | 11 |
| 8.5 | 13 |
| 9 | 20 |
| 8 | 10 |
| 5.5 | 10 |
On a scatter plot, the table would be plotted as (x, y) points, with the first column being the x values (foot size) and the second column being the y values (arm length). In this particular example, the data points are all over the graph because there is no correlation between foot size and arm length.
There is no pattern to the data, neither positive nor negative, so this is a no correlation graph or a no association scatter plot. This type of graph indicates that there is no relationship/association from one data point to the next in the graph.
Strong Linear Relationship: Negative Correlation
Another type of scatter plot is the strong linear relationship graph with negative correlation. In this type of graph, there is a straight line that comfortably fits through the data, indicating a strong linear relationship between the variables. The slope of the line is also negative (small values of X correspond to large values of Y; large values of X correspond to small values of Y), so there is a negative correlation between X and Y.
Example: Sam measured the height and petal length (in centimeters) of all the flowers in his garden. The data is shown in the scatter plot below.
| Height (cm) | Petal length (cm) |
|---|---|
| 30 | 6 |
| 20 | 4 |
| 15 | 2 |
| 40 | 8 |
| 50 | 12 |
In this scatter plot, there is a strong linear relationship between the height of the flowers and their petal length. The line has a negative slope, indicating that as the height of the flower increases, its petal length decreases.
Positive Association
A positive association in a scatter plot indicates that as one variable increases, the other variable also tends to increase. This type of graph is characterized by a straight line with a positive slope (large values of X correspond to large values of Y; small values of X correspond to small values of Y).
Example: Dexter's class recorded data on the test grades and shoe sizes of students in the class. The data is shown in the scatter plot below.
| Shoe size | Test score |
|---|---|
| 5 | 60 |
| 6 | 70 |
| 7 | 80 |
| 8 | 90 |
| 9 | 100 |
In this scatter plot, there is a positive association between shoe size and test score. As the shoe size increases, the test score also tends to increase.
##Scatter plots are a powerful tool used to visualize relationships between two variables. By understanding the different types of scatter plots, such as no correlation graphs, strong linear relationship graphs with negative correlation, and positive association graphs, we can gain insights into the relationships between variables and make informed decisions based on that information.