1. Meaning of a Scatter Diagram
A scatter diagram is a graph that shows how two quantities are related. Each pair of values is marked as a point on the graph. By looking at the overall pattern of the points, we can understand whether the two variables move together or not.
Scatter diagrams help visualize correlation without using formulas.
2. How to Plot a Scatter Diagram
A scatter diagram is drawn using pairs of values (x, y). Each pair represents one observation.
Steps to draw it:
- Choose the two variables you want to compare.
- Mark one variable along the horizontal axis (x-axis) and the other along the vertical axis (y-axis).
- For each pair of values, plot a point at the position matching its x and y values.
- Look at the overall pattern formed by the points.
2.1. Example
Suppose the temperature (°C) and ice-cream sales are recorded:
| Temperature (x) | Sales (y) |
|---|---|
| 25 | 40 |
| 28 | 52 |
| 30 | 60 |
| 33 | 72 |
Plot each pair. The points will rise from left to right, suggesting a positive relationship.
3. Patterns in Scatter Diagrams
The shape made by the points helps show the type of correlation. Even without calculating any number, the pattern gives a clear idea of the relationship between the two variables.
3.1. Positive Correlation Pattern
If the points move upward from left to right, the two variables increase together. More of x means more of y.
Example: hours studied and marks scored.
3.2. Negative Correlation Pattern
If the points move downward from left to right, one variable increases while the other decreases.
Example: speed of a vehicle and time taken to reach a place.
3.3. No Correlation Pattern
If the points have no clear pattern and are scattered randomly, there is no relationship between the two variables.
Example: shoe size and reading habit.
4. Uses of Scatter Diagrams
Scatter diagrams are widely used because they give an instant visual idea of how two variables behave together. They help in:
- Identifying correlation type
- Spotting outliers
- Predicting trends
- Checking whether a linear model might fit the data