Scatter Plots
What is a Scatter Plot?
A scatter plot (scatter diagram) displays two variables for the same set of data, with each variable on one axis. Each observation becomes a single point on the graph.
Use scatter plots to look for relationships (correlation) between variables โ for example, whether taller people tend to have larger shoe sizes.
Key terms:
- x-axis (horizontal): the independent variable (what you control or measure first)
- y-axis (vertical): the dependent variable (what you observe)
- Data point: each individual observation plotted as a dot
Types of Correlation
Positive correlation: as x increases, y tends to increase โ points slope from bottom-left to top-right.
- Example: height and shoe size; hours studied and test score
Negative correlation: as x increases, y tends to decrease โ points slope from top-left to bottom-right.
- Example: altitude and temperature; speed and journey time
No correlation: no clear pattern โ points are scattered randomly across the graph.
- Example: shoe size and IQ score
Strength of Correlation
Strong correlation: points cluster closely around an imaginary line โ easy to predict one variable from the other.
Weak correlation: points show a general trend but are spread out โ predictions are less reliable.
Perfect correlation: all points lie exactly on a straight line (rare in real data).
The correlation coefficient (r) gives a number between -1 and 1:
- r = 1: perfect positive
- r = -1: perfect negative
- r = 0: no correlation
- r close to 0.8 or -0.8 indicates strong correlation
Line of Best Fit
A line of best fit (trend line) summarises the overall trend through the data. Rules for drawing it:
- The line should pass through the mean point (xฬ, ศณ) โ the average of all x-values paired with the average of all y-values
- Aim for roughly equal numbers of points above and below the line
- The line does not need to pass through any specific data point
- Extend it to cover the range of the data
Making Predictions
Use the line of best fit to estimate values:
Interpolation: predicting a y-value for an x-value within the data range. This is reliable.
Extrapolation: predicting beyond the data range. This is less reliable โ trends may not continue outside the measured range.
Example: if your line shows that 5 hours of revision predicts a score of 65%, you can read off an estimate for 6 hours of revision (interpolation within range).
Worked Example
A student records revision time (hours) and percentage score for 8 classmates:
| Hours | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Score | 42 | 50 | 55 | 60 | 68 | 72 | 78 | 80 |
The mean point is approximately (4.5, 63). Draw a line through this point with roughly equal points on each side. To predict the score for 5.5 hours, read off the y-value from the line.
Outliers
An outlier is a data point that lies far from the general trend. It may be:
- A genuine exception worth investigating
- A measurement or recording error
Do not simply delete outliers โ investigate them first and mention them when describing the scatter plot.
Correlation vs Causation
Just because two variables are correlated does not mean one causes the other. Both may be influenced by a third variable (confounding factor).
Classic example: ice cream sales and drowning rates are positively correlated โ both rise in summer. Hot weather causes both; ice cream does not cause drowning.
Always ask: "Could a third variable explain this correlation?"
Common Mistakes
- Drawing the line of best fit so it passes through the origin when the data does not support it
- Confusing correlation with causation
- Extrapolating far beyond the data range and treating the prediction as reliable
- Forgetting to plot every data point
- Drawing a curved line of best fit when a straight line fits the data better
Tips and Tricks
- Always label both axes with the variable name and units
- Use a ruler to draw the line of best fit โ a freehand curve will lose marks
- The line of best fit does not have to pass through any actual data point
- When asked to describe the correlation, state the type (positive/negative/none) AND the strength (strong/weak)
- To find the mean point: calculate the mean of all x-values and the mean of all y-values separately