Appears in: Functional Skills Level 2 · GCSE foundation
Scatter graphs and correlation
A scatter graph plots two measurements for each item — hours revised and marks scored, temperature and ice-cream sales — as one dot each. The questions ask you to describe the pattern, draw a line through it and use that line to estimate. There's almost no calculation; the marks are for reading carefully and using the right words.
What the examiner wants
- Describe the correlation. Dots rising from bottom-left to top-right: positive correlation. Falling from top-left to bottom-right: negative correlation. No pattern: no correlation. Add 'strong' or 'weak' by how tightly the dots hug a line.
- Interpret it in context. 'As temperature increases, ice-cream sales increase.' Correlation is not cause — say 'is associated with', not 'makes'.
- Draw a line of best fit: a single straight line, with roughly as many points above as below, following the trend. It does not have to pass through the origin or through any particular point.
- Use the line to estimate: read across from a value on one axis to the line, then down (or across) to the other axis. Show the lines you drew — that's where the method mark is.
- Spot outliers: a point far from the trend. Mention it, and leave it out when drawing the line if the question tells you to.
Worked examples
Example 1
A scatter graph of hours revised against test marks shows the dots rising steadily from bottom-left to top-right. Describe the correlation and what it means.
- Positive correlation.
- The more hours a learner revised, the higher their test mark tended to be.
Example 2
On the same graph the line of best fit passes through (2, 30) and (8, 60). Estimate the mark for a learner who revised for 5 hours.
- 5 hours is halfway between 2 and 8, so the estimate is halfway between 30 and 60.
- Estimated mark: 45. (Reading up from 5 on the hours axis to the line, then across.)
Where the marks go missing
- Describing a correlation as 'they go up together' without using the word positive (or negative). Use the vocabulary.
- Joining the dots, or drawing a line that starts at the first point and ends at the last. A line of best fit is one straight line through the middle of the trend.
- Extrapolating: estimating far beyond the plotted data and treating the answer as reliable. Say it's less reliable, and the mark is yours.
Frequently asked questions
What does positive correlation mean on a scatter graph?
As one variable increases, the other tends to increase too, so the points run from bottom-left to top-right. Negative correlation is the opposite: one goes up as the other goes down.
How do you draw a line of best fit?
Draw one straight line that follows the trend of the points, with roughly equal numbers of points on either side. Ignore obvious outliers. It doesn't need to go through the origin.