How do you tell the difference between a strong and a weak association on a scatter plot?

Look at how close the dots are to forming a straight line. If the points cluster tightly along a line, the association is strong. If they are spread far apart with only a rough trend visible, the association is weak. When the dots look completely random with no trend, there is no association at all.

Scatter Plot — Definition, Formula & Examples

A scatter plot is a graph that uses dots on a coordinate plane to show how two sets of numbers are related. Each dot represents one data pair, with one value on the x-axis and the other on the y-axis.

A scatter plot is a statistical graph that displays bivariate data as a set of ordered pairs $(x, y)$ plotted in the Cartesian plane, where the horizontal axis represents the independent variable and the vertical axis represents the dependent variable. The resulting pattern of points reveals the direction, form, and strength of any association between the two variables.

How It Works

To create a scatter plot, you need two measurements for each item in your data set — for example, a student's hours of study and their test score. Plot each pair as a single point on the coordinate plane. Once all points are plotted, look at the overall pattern. If the dots trend upward from left to right, there is a positive association (as one variable increases, so does the other). If they trend downward, there is a negative association. If the dots show no clear direction, there is no association. You can also judge the strength of the relationship by how tightly the points cluster together.

Worked Example

Problem: Five students recorded the number of hours they studied and their test scores. Plot the data and describe the association. Hours studied: 1, 2, 3, 4, 5 Test scores: 55, 60, 72, 78, 90

Step 1: Write each data pair as an ordered point.

(1, 55),\; (2, 60),\; (3, 72),\; (4, 78),\; (5, 90)

Step 2: Draw a coordinate plane. Label the x-axis "Hours Studied" (scale 0 to 6) and the y-axis "Test Score" (scale 50 to 100).

Step 3: Plot each ordered pair as a dot on the plane. For example, the point (1, 55) goes 1 unit right and 55 units up.

Step 4: Observe the pattern. The dots rise from left to right, so there is a positive association: more hours of study are linked to higher test scores.

Answer: The scatter plot shows a positive association between hours studied and test scores.

Another Example

Problem: A teacher records the daily high temperature (°F) and the number of hot chocolates sold at the school café for six days: Temperature: 30, 40, 50, 55, 65, 75 Hot chocolates sold: 45, 38, 30, 25, 15, 8

Step 1: Write the ordered pairs.

(30, 45),\; (40, 38),\; (50, 30),\; (55, 25),\; (65, 15),\; (75, 8)

Step 2: Plot each point on a coordinate plane with Temperature on the x-axis and Hot Chocolates Sold on the y-axis.

Step 3: The dots fall from left to right. As temperature increases, sales decrease.

Answer: The scatter plot shows a negative association — higher temperatures correspond to fewer hot chocolate sales.

Visualization

Why It Matters

Scatter plots are a core topic in 8th-grade math and introductory statistics courses. Scientists use them to spot trends in experimental data, such as whether a new fertilizer increases plant growth. Being able to read and interpret scatter plots also prepares you for learning about lines of best fit and correlation in algebra and high school statistics.

Common Mistakes

Mistake: Connecting the dots with lines as if it were a line graph.

Correction: Scatter plots leave the dots unconnected. The purpose is to show the overall pattern of the data, not to suggest a continuous path between points.

Mistake: Mixing up which variable goes on which axis.

Correction: The independent variable (the one you control or that happens first) goes on the x-axis, and the dependent variable (the outcome you measure) goes on the y-axis. Swapping them can make the graph misleading.