What is a scatter plot?
Sometimes we measure two things about the same person or object, like height and weight. These are paired data (bivariate data). A scatter plot puts one quantity on the x-axis and the other on the y-axis and draws one dot for each pair.
How to make one:
- Choose which variable goes on x (often the one that might cause the change) and which on y.
- Pick a scale for each axis that fits all the values. Label the axes with names and units.
- Plot each pair (x, y) as a dot. Do not join the dots.
Positive, negative and no association
Positive association: as x increases, y tends to increase. The dots rise from left to right. Example: height and arm span.
Negative association: as x increases, y tends to decrease. The dots fall from left to right. Example: age of a car and its resale price.
No association: no clear up or down pattern. Example: shoe size and maths score.
Strength: if the dots lie close to a line, the association is strong; if they are widely spread, it is weak.
Linear or non-linear: if the dots follow a straight line, it is linear. If they follow a curve (for example, rising then falling), it is non-linear.
Clusters and outliers
A cluster is a group of dots that sit close together, with gaps around them. Clusters can show two different kinds of data in one plot, for example adults and children.
An outlier is a dot far away from the general pattern. It may be a mistake in the data, or something special really happened. Always check outliers before drawing a conclusion.
Association is not causation
Two things moving together does not prove one causes the other. Ice-cream sales and swimming accidents both rise in summer, but ice cream does not cause accidents: hot weather drives both. Say "is associated with", not "causes", unless an experiment shows it.
Try it
Measure the height and hand span of 8 family members or friends. Make a table, then draw a scatter plot on graph paper. Is the association positive? Is there an outlier? In the 3D, pick each data set and slide the spread from 0 to 3 to see strong turn into weak.
Key formulas and definitions
- Point = (x, y): one dot per pair
- Positive: y tends to rise as x rises
- Negative: y tends to fall as x rises
- Cluster: a clump of dots; Outlier: a dot far from the pattern
Worked examples
1. A table gives (hours of practice, goals scored): (1, 2), (2, 3), (3, 5), (4, 6), (5, 8). Describe the association.
Plot the five dots. As practice hours go up, goals go up, and the dots lie close to a straight line. So it is a strong positive linear association.
2. Car age (years) and price (in thousands): (1, 700), (3, 560), (5, 410), (7, 300), (9, 190). Describe it.
As age increases, price decreases. The dots fall to the right fairly evenly, so it is a negative linear association.
3. Data on study hours vs score: (2, 50), (3, 58), (4, 63), (5, 71), (6, 15), (7, 84). Which point is an outlier and what might explain it?
All points rise steadily except (6, 15), which is far below the pattern. It is an outlier. Perhaps the student was ill, or the score was entered wrongly.
Common mistakes
- Joining the dots with lines like a line graph. A scatter plot keeps separate dots.
- Saying "x causes y" just because the dots show an association.
- Using uneven scales on an axis, which bends the pattern.
- Calling a plot "no association" when it is actually a curve (non-linear).