Key takeaway: A scatter plot turns paired measurements into dots on a grid, making it easy to spot whether two quantities move together and in what pattern.
Grade 88.SP.A.1Statistics and Data
Definition of Scatter Plot
A scatter plot displays two numerical variables at once. Each dot stands for one person, day or object, with its horizontal position given by one variable and its vertical position by the other.
The overall shape of the dots tells the story. Dots climbing toward the upper right mean a positive association. Dots sliding toward the lower right mean a negative one. A shapeless cloud means none. Dots that gather together form a cluster, and a dot far from the rest is an outlier. A pattern can be linear, following a straight band, or nonlinear, bending like a curve.
Formula and notation
Every dot is an ordered pair that lists the input variable first:
\[(x, y) = (\text{temperature}, \text{cups sold})\]
Label both axes with the variable name and unit, choose an even scale, and give the scatter plot a title. Nothing is connected: the points stay separate.
Key facts
- Rising dots signal positive association, and falling dots signal negative association.
- A tight band of dots means a strong association; a loose spread means a weak one.
- One dot lying well away from the main band is an outlier.
- A scatter plot shows association, not proof that one variable causes the other.
Scatter Plot example
A food truck records the daily high temperature (°F) and the cups of lemonade sold: (68, 41), (72, 50), (75, 52), (81, 66), (84, 71), (88, 80), (93, 92). Describe the association in a scatter plot of these data.
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Put temperature on the horizontal axis and cups sold on the vertical axis, then plot the seven points.
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As the temperature goes from 68 to 93, cups sold go from 41 to 92, so the points rise to the right.
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The points stay close to one straight band and no dot is far from the rest.
The plot shows a strong positive linear association with no outliers.
Common mistake
Watch out
A scatter plot of shoe size against reading score for elementary students rises to the right, and Jonah concludes that bigger feet make kids read better.
Why it is wrong
Association is not causation. Both variables grow with a third one, age. Older students have bigger feet and read better. A scatter plot can reveal a pattern, but it cannot show why the pattern occurs.
Related terms and lessons
- Grade 8 · Scatter Plots and AssociationLessonWorksheetQuiz
- Algebra 1 · Two-Way Tables, Scatter Plots and CorrelationLessonWorksheetQuiz
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