How to graph Scatter Plots? (+FREE Worksheet!)

A scatter plot is a graph that shows the relationship between two sets of data by plotting ordered pairs on a coordinate plane. Each point represents one observation with an x-value and a y-value. Scatter plots are a powerful tool in Algebra 1 for spotting trends, identifying correlations, and drawing a line of best fit. This lesson walks you through how to create and interpret scatter plots, with clear examples and practice problems.

What Is a Scatter Plot?

A scatter plot (also called a scatterplot or scatter diagram) displays two-variable data as a collection of points on a coordinate grid. The independent variable (the one you control or measure first) goes on the x-axis; the dependent variable (the one that responds) goes on the y-axis. Once you plot all the points, you look at the overall pattern to decide if the two variables are related.

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How to Graph a Scatter Plot

Step 1: Set Up the Axes

Choose a scale for both axes so all data points fit comfortably. Label each axis with the variable name and units.

Step 2: Plot Each Ordered Pair

For each row of data, locate the x-value on the horizontal axis and the corresponding y-value on the vertical axis, then place a point (dot) at that position. Example: the pair (3, 7) means \(\color{blue}{x = 3}\), \(\color{blue}{y = 7}\).

Step 3: Identify the Correlation

Look at the overall direction of the points:

• Positive correlation: Points trend upward from left to right (as x increases, y increases).
• Negative correlation: Points trend downward from left to right (as x increases, y decreases).
• No correlation: Points are scattered with no clear direction.

Correlation can also be described as strong (points close to a line) or weak (points spread out).

Step 4: Draw a Line of Best Fit (Trend Line)

A line of best fit is a straight line drawn through the scatter of points so that roughly equal numbers of points lie above and below the line. It summarizes the trend and can be used to make predictions.

Step-by-Step Summary

1. Label the x-axis (independent variable) and y-axis (dependent variable); choose an appropriate scale.
2. Plot each data pair as a point (x, y) on the coordinate grid.
3. Look at the pattern: positive correlation, negative correlation, or no correlation.
4. Draw a line of best fit (trend line) that balances points above and below it.
5. Use the line of best fit to make predictions within or near the data range.

Watch: Constructing a Scatter Plot (Video Lesson)

Khan Academy demonstrates how to construct a scatter plot from a data table:

Scatter Plots – Worked Examples

Example 1: The table shows hours studied (x) and test scores (y) for 5 students: (1, 55), (2, 65), (3, 70), (4, 80), (5, 90). Describe the correlation.

As hours studied increase, test scores increase. The points trend upward from left to right. This is a strong positive correlation.

Example 2: A scatter plot shows outdoor temperature (x) and cups of hot chocolate sold (y). As temperature increases, sales decrease. What type of correlation is this?

As x increases, y decreases. This is a negative correlation.

Example 3: Data: (2, 8), (4, 5), (6, 9), (8, 3), (10, 7). Describe the correlation.

The points show no consistent upward or downward trend — they are scattered randomly. This data set shows no correlation.

Example 4: A line of best fit for a scatter plot of (hours of TV watched, GPA) passes through the points (1, 3.8) and (5, 2.2). If a student watches 3 hours of TV per day, predict their GPA using the line.

\(\color{blue}{\text{ Slope } = (2.2 – 3.8)}\) ÷ \(\color{blue}{(5 – 1) = (-1.6)}\) ÷ 4 = −0.4
Using point (1, 3.8): y = −\(\color{blue}{0.4x + b}\) → 3.8 = −\(\color{blue}{0.4(1) + b}\) → \(\color{blue}{b = 4.2}\)
At \(\color{blue}{x = 3}\): y = −\(\color{blue}{0.4(3) + 4.2}\) = −\(\color{blue}{1.2 + 4.2}\) = 3.0

More Practice: Scatter Plots Explained (Video Lesson)

Simplifying Math provides an additional walkthrough of scatter plots, correlation, and lines of best fit:

Exercises: Scatter Plots

1. The points (1, 2), (2, 5), (3, 4), (4, 8), (5, 7) are plotted. Is the correlation positive, negative, or none? Explain.
2. A scatter plot of shoe size vs. height shows points trending upward. Describe the type and direction of correlation.
3. A scatter plot of car age (years) vs. resale value ($) shows points trending downward. What type of correlation is this?
4. Plot the points (0, 1), (1, 3), (2, 5), (3, 7), (4, 9) on a coordinate grid and draw a line of best fit. What is the equation of the line?
5. A line of best fit passes through (2, 10) and (6, 2). Predict the y-value when \(\color{blue}{x = 4}\).
6. Explain why a scatter plot with all points forming a perfect diagonal line is considered a perfect correlation.

Answers

1. Positive correlation: as x increases, y generally increases.
2. Strong positive correlation: larger shoe sizes tend to go with taller heights.
3. Negative correlation: as car age increases, resale value decreases.
4. The points form a perfect line. \(\color{blue}{\text{ Slope } = (9-1)}\)÷\(\color{blue}{(4-0) = 2}\); equation is \(\color{blue}{y = 2x + 1}\).
5. \(\color{blue}{\text{ Slope } = (2-10)}\)÷(\(\color{blue}{6-2}\)) = −8÷4 = −2; equation: y = −\(\color{blue}{2x + 14}\); at \(\color{blue}{x=4}\): y = −\(\color{blue}{2(4)+14}\) = 6
6. Every point lies exactly on the line of best fit, so the relationship is perfectly linear — there is zero deviation from the trend.

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Frequently Asked Questions

What does a line of best fit tell you?

A line of best fit (trend line) shows the general linear trend of the data and lets you make predictions. Points above the line have actual y-values higher than the trend predicts; points below have lower actual values. It minimizes the overall distance from the data points to the line.

What is the difference between correlation and causation?

Correlation means two variables tend to change together. Causation means one variable directly causes the other to change. A scatter plot can show correlation but cannot prove causation — a third unrelated factor may be responsible for the pattern.

When is a scatter plot not the right graph to use?

Use a scatter plot only when both variables are numerical and you want to explore the relationship between them. If one variable is categorical (e.g., color, name) or you are comparing totals across groups, a bar graph or pie graph is more appropriate.

Related Topics

• Mean, Median, Mode, and Range
• Pie Graph
• Probability Problems
• Statistics
• Linear Equations