Scatter Diagram — Definition, Formula & Examples
A scatter diagram is a graph that shows the relationship between two sets of numerical data by plotting each data pair as a point on a coordinate plane.
A scatter diagram is a two-dimensional graphical representation in which each observation of a bivariate data set is plotted as an ordered pair on a Cartesian coordinate system, used to visually assess the direction, form, and strength of the association between two quantitative variables.
How It Works
To create a scatter diagram, choose which variable goes on the horizontal axis () and which goes on the vertical axis (). Plot each data pair as a single dot at the corresponding coordinates. Once all points are plotted, look at the overall pattern. If the points trend upward from left to right, the variables have a positive association. If they trend downward, the association is negative. If the points show no clear direction, the variables may have little or no association.
Worked Example
Problem: Five students reported how many hours they studied for a test and their test scores: (1, 55), (2, 60), (3, 70), (4, 80), (5, 90). Describe the association shown by a scatter diagram of this data.
Step 1: Label the horizontal axis "Hours Studied" (values 0–6) and the vertical axis "Test Score" (values 50–100).
Step 2: Plot each ordered pair as a point: (1, 55), (2, 60), (3, 70), (4, 80), (5, 90).
Step 3: Observe that as hours increase, test scores also increase. The points rise from left to right in a roughly straight line.
Answer: The scatter diagram shows a strong positive linear association between hours studied and test score.
Visualization
Why It Matters
Scatter diagrams are one of the first tools you learn for exploring whether two variables are related, which is foundational in science fair projects, social studies data analysis, and later courses in algebra and statistics. Doctors, economists, and engineers all use scatter plots to spot trends before running formal calculations like correlation or regression.
Common Mistakes
Mistake: Connecting the dots with a line as if it were a line graph.
Correction: Leave the points unconnected. A scatter diagram shows individual data pairs, not a continuous sequence. You may add a trend line (line of best fit), but you should not connect point to point.