Scatter Diagrams and Correlation
Simple Explanation
A scatter diagram plots paired data (x,y) as individual points, revealing whether two variables are related. Positive correlation: points trend upward (as x increases, y tends to increase). Negative correlation: points trend downward. No correlation: points show no clear pattern.
Why Do We Need It?
A quick glance at a scatter diagram often reveals a relationship (or lack of one) between two variables far faster than examining a table of raw numbers.
See It
A scatter plot of points trending upward from lower-left to upper-right, showing positive correlation
Worked Example
Classify the type of correlation
A scatter diagram shows that as students study more hours, their test scores tend to be higher. What type of correlation is this?
Why Does This Work?
Correlation type is defined entirely by the overall trend direction visible in the scattered points — an upward-sloping pattern of points is defined as positive correlation, and a downward-sloping pattern as negative, regardless of how tightly or loosely the points cluster around that trend.
Real-Life Example
Ice cream sales versus temperature
A shop records daily ice cream sales alongside the day's temperature.
A scatter diagram of this data would show positive correlation — hotter days tend to have higher sales — visible immediately from the pattern of points.
Practice
A scatter diagram shows that as a car's age increases, its resale value tends to decrease. What type of correlation is this?
MediumCommon mistake
Assuming correlation proves one variable directly causes the other — correlation only describes an observed pattern, and does not by itself establish cause and effect.
Quick Review
- Positive correlation: points trend upward.
- Negative correlation: points trend downward.
- No correlation: no clear directional pattern.