A scatter graph plots two variables against each other to show whether they are related. Points rising from left to right indicate positive correlation; points falling indicate negative correlation; no clear pattern means no correlation. The line of best fit passes through the mean point and balances points above and below it.
What are the types of correlation?
Correlation describes whether two variables tend to increase or decrease together. There are three types:
| Type | Description | Example |
|---|---|---|
| Positive | As x increases, y increases | Height and shoe size |
| Negative | As x increases, y decreases | Hours of TV watched and exam score |
| No correlation | No pattern between x and y | Eye colour and maths grade |
Each type can be strong (points close to a line) or weak (points widely scattered). A strong positive correlation gives a tight cluster along a line rising to the right; a weak positive correlation shows the same overall trend but with a lot of scatter.
How do you draw a scatter graph?
- Label both axes with the variable name and its units (e.g. height (cm), mass (kg)).
- Choose a sensible scale that uses most of the graph area.
- Plot each pair of values as a cross (×), one pair at a time.
- Do not join the points — scatter graphs are not line graphs.
- Check your plots against the original table before moving on.
The scale does not need to start at zero if all values are bunched together; a broken axis (shown with a zigzag) is acceptable.
How do you draw and use the line of best fit?
The line of best fit is a straight line drawn by eye to represent the trend. To draw it correctly:
- Find the mean of the x-values (x̄) and the mean of the y-values (ȳ).
- Plot the mean point (x̄, ȳ) — the line of best fit MUST pass through it.
- Draw the line so that it has roughly equal numbers of data points above and below it.
- Extend the line across the data range (do not force it through the origin unless the data suggests it).
Worked example: A student collects data on revision time (hours) and test score (%) for 8 classmates:
| Revision (h) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Score (%) | 42 | 48 | 55 | 61 | 64 | 70 | 75 | 81 |
Mean revision = (1+2+3+4+5+6+7+8)/8 = 36/8 = 4.5 h
Mean score = (42+48+55+61+64+70+75+81)/8 = 496/8 = 62%
The line of best fit passes through (4.5, 62). Draw a ruler line through this point following the upward trend.
What is interpolation and what is extrapolation?
Once you have the line of best fit, you can use it to estimate values.
- Interpolation — reading off a value within the range of the data. For the example above, estimating the score for someone who revised 3.5 hours is interpolation (the data spans 1–8 hours). Interpolation is reasonably reliable.
- Extrapolation — extending the line beyond the data range to estimate a value outside it. For example, predicting the score for 12 hours of revision. Extrapolation is less reliable because we do not know the trend continues in the same way.
Exam questions often ask you to comment on reliability. Always mention whether you are interpolating or extrapolating.
What is the difference between correlation and causation?
Just because two variables are correlated does not mean one causes the other. This is one of the most important ideas at GCSE.
Example: There is a strong positive correlation between the number of ice creams sold and the number of drowning incidents. Does eating ice cream cause drowning? No — both are caused by a third variable: hot sunny weather. This is called a lurking variable or confounding factor.
When asked to interpret a scatter graph, you may say: "There is a strong positive correlation between revision time and test score, suggesting that more revision is associated with a higher score." Avoid saying "more revision causes a higher score" unless you have evidence beyond the graph.
What does a GCSE exam question on scatter graphs look like?
Typical GCSE questions include:
| Task | What to do |
|---|---|
| Describe the correlation | State type (positive/negative/none) and strength (strong/weak) |
| Draw the line of best fit | Find and plot the mean point; draw a balanced line through it |
| Use the line to estimate | Read off the graph; state whether this is interpolation or extrapolation |
| Comment on reliability | Interpolation: reasonably reliable; extrapolation: less reliable |
| Identify an outlier | Point clearly away from the trend; may have an unusual value for one or both variables |
An outlier is a point that does not fit the overall pattern. You should identify it but do not remove it from the data without a reason (e.g. a recording error).
Frequently asked questions
Can the line of best fit be curved?
At GCSE, the line of best fit is always a straight line. Curved lines of best fit exist in statistics but are beyond the GCSE specification. If the scatter diagram shows a clear curve (e.g. an arch shape), you would still draw a straight line for GCSE purposes and note that a linear model may not be the best fit.
What if the line of best fit goes through the origin?
Only draw the line through the origin if the data actually suggests this — for example, if zero x gives zero y and the scatter confirms it. Do not force the line through the origin just because the axes start at zero. The mean point is your anchor, not the origin.
How many points should be above and below the line of best fit?
Aim for a roughly equal number, but the key requirement is that the line passes through the mean point (x̄, ȳ). In a set of 8 data points, having 4 above and 4 below is ideal, but 3 and 5 is perfectly acceptable if the line passes through the mean point and follows the trend.
Does a strong correlation mean the relationship is important?
Not necessarily. A very strong correlation might exist over a very narrow range, or between two variables that share a common cause. Strength of correlation tells you how well the points cluster around the line — it says nothing about whether the relationship is meaningful or causal. Always interpret correlation in context.
Professor Pi can walk you through GCSE scatter graph questions one step at a time — try it at aitutors.me.