What type of correlation is shown when points trend upwards?
As one increases, the other increases.
Upward trend = positive correlation.
Scatter Graphs
Scatter graphs show the relationship between two variables. They are used to identify patterns such as positive or negative correlation.
Overview
A scatter graph is used to investigate the relationship between two variables.
Each point represents one pair of values.
One point = one pair of related data values
Scatter graphs help you spot patterns, describe correlation, and estimate values using a line of best fit.
What you should understand after this topic
- Plot points on a scatter graph
- Understand what positive, negative and no correlation mean
- Recognise strong and weak correlation
- Draw a line of best fit
- Make sensible predictions from the graph
Key Definitions
Scatter Graph
A graph showing pairs of data values as plotted points.
Variable
A quantity that can change, such as height, time or score.
Correlation
A relationship or pattern between two variables.
Positive Correlation
As one variable increases, the other tends to increase.
Negative Correlation
As one variable increases, the other tends to decrease.
No Correlation
There is no clear pattern between the variables.
Line of Best Fit
A straight line drawn to show the overall trend of the data.
Outlier
A point that does not fit the general pattern.
Key Rules
Plot each pair carefully
Each point comes from one x-value and one y-value.
Look for a pattern
Decide whether the points go up, down or show no trend.
Use a best fit line
Draw it through the middle of the points, not through every point.
Be careful with predictions
Interpolating is safer than extrapolating.
Correlation Types
Positive correlation
Points rise from left to right.
Negative correlation
Points fall from left to right.
No correlation
Points are scattered with no clear direction.
Strong or weak
The closer the points are to a line, the stronger the correlation.
How to Solve
What is a scatter graph?
A scatter graph shows the relationship between two variables. Each point represents a pair of values, such as hours revised and test score.
How to read data pairs
\((1,42), (2,48), (3,55), (4,61), (5,68)\)
Each pair represents one point.
First value = x-coordinate (horizontal axis).
Second value = y-coordinate (vertical axis).
Step 1: Plot the points
Put the first variable on the x-axis.
Put the second variable on the y-axis.
Plot each pair accurately as a point.
Step 2: Describe the correlation
Look at the overall pattern formed by the points.
Positive correlation
As x increases, y increases.
Negative correlation
As x increases, y decreases.
No correlation
No clear pattern between x and y.
Strong correlation
Points lie close to a straight line.
Step 3: Draw a line of best fit
The line of best fit shows the overall trend of the data.
Draw a straight line through the middle of the points.
There should be roughly equal numbers of points above and below the line.
Do not join dot-to-dot.
Step 4: Use the line to estimate
Use the line of best fit to estimate unknown values.
Find the x-value on the axis.
Move up or down to the line.
Read the corresponding y-value.
Interpolation and extrapolation
Interpolation
Estimating within the data range (more reliable).
Extrapolation
Estimating outside the data range (less reliable).
Outliers
An outlier is a point that does not follow the general pattern.
Identify the outlier.
Do not let it distort your line of best fit.
Exam tip: Mention the outlier if asked about reliability.
Exam thinking: correlation and cause
A relationship between variables does not always mean one causes the other.
Two variables can be linked without one causing the other.
Example: Hot weather increases both ice cream sales and sun cream sales.
Scatter graphs are often used to compare data collected using sampling.
Exam method summary
See bar charts for other ways to display data.
- Plot points accurately.
- Describe the correlation.
- Draw a sensible line of best fit.
- Use the line to estimate values.
- Comment on reliability (outliers, interpolation vs extrapolation).
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on identifying correlation from scatter graphs.
Edexcel
The scatter graph shows the relationship between revision time and test score.
Describe the correlation shown by the scatter graph.
Edexcel
The points on a scatter graph have no clear pattern.
State the type of correlation shown.
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on lines of best fit and predictions.
AQA
The scatter graph shows the relationship between temperature and the number of hot drinks sold.
Use the line of best fit to describe the correlation.
AQA
What is a line of best fit used for on a scatter graph?
AQA
A point lies far away from the overall pattern on a scatter graph.
What is this point called?
OCR
Exam-style questions aligned with OCR GCSE Mathematics, emphasising interpretation, outliers and reliability of predictions.
OCR
The scatter graph shows the relationship between the age of a car and its value.
Identify the outlier on the graph and describe the correlation shown by the other points.
OCR
A prediction is made using a line of best fit outside the range of the data.
Explain why this prediction may be unreliable.
OCR
Which is usually more reliable: interpolation or extrapolation? Give a reason for your answer.
Exam Checklist
Step 1
Plot each coordinate pair carefully.
Step 2
Look for the overall pattern in the points.
Step 3
Describe the correlation accurately.
Step 4
Draw a sensible line of best fit if needed.
Most common exam mistakes
Wrong coordinates
Plotting points in the wrong place.
Wrong correlation
Mixing up positive and negative correlation.
Bad best fit line
Drawing the line through one edge of the points instead of the middle.
Unsafe prediction
Extrapolating too far beyond the data range.
Common Mistakes
These are common mistakes students make when working with scatter graphs in GCSE Maths.
Plotting coordinates in the wrong order
Incorrect
A student swaps the x- and y-values when plotting points.
Correct
Coordinates are written as (x, y). Always move horizontally first (x-axis), then vertically (y-axis).
Misidentifying correlation
Incorrect
A student says the correlation is positive when it is negative, or vice versa.
Correct
Positive correlation means both variables increase together. Negative correlation means one increases while the other decreases.
Forcing the line through every point
Incorrect
A student draws a line connecting all points exactly.
Correct
A line of best fit should show the overall trend, not pass through every point. It should balance the data.
Ignoring outliers
Incorrect
A student includes extreme points when drawing the line of best fit.
Correct
Identify and consider outliers separately, as they can distort the trend.
Making unreliable extrapolations
Incorrect
A student predicts values far beyond the data range.
Correct
Extrapolation becomes less reliable the further you go beyond the data. Keep predictions close to the known values.
Try It Yourself
Practise interpreting scatter graphs and lines of best fit.
Foundation
Foundation Practice
Identify correlation and interpret scatter graphs.
What type of correlation is shown when points trend downwards?
As one increases, the other decreases.
Downward trend = negative correlation.
If points show no clear pattern, what type of correlation is it?
Random pattern.
No clear pattern = no correlation.
A graph shows height vs shoe size increasing together. What type of correlation?
Both increase.
This is positive correlation.
What does a line of best fit show?
Think trend.
It shows overall pattern.
If hours studied increases and test score increases, what correlation?
Both increase.
Positive correlation.
What is an outlier?
Unusual value.
Outliers are unusual points.
If temperature increases and heating cost decreases, what correlation?
One increases, other decreases.
Negative correlation.
Which graph shows strong correlation?
Think closeness.
Closer points = stronger correlation.
If no pattern is visible, what correlation?
Random.
No correlation.
Higher
Higher Practice
Use scatter graphs to estimate values and interpret trends.
A line of best fit is used to:
Think estimation.
Used for predictions.
If a line of best fit shows upward trend, what type of correlation?
Think direction.
Upward = positive.
What is interpolation?
Inside range.
Interpolation = inside data.
What is extrapolation?
Outside data range.
Extrapolation is beyond data.
Why is extrapolation less reliable?
Think unknown area.
Less reliable outside data.
If data shows strong negative correlation, describe the trend.
Downward trend.
Strong negative = decreasing trend.
A student draws line through all points exactly. What is wrong?
Best fit balances data.
Line should not hit every point.
If correlation is weak, how are points arranged?
Not close to line.
Points are widely spread.
Which situation likely shows positive correlation?
Think real-world.
Height and shoe size increase together.
If a line slopes downwards, what type of correlation?
Downward trend.
Negative correlation.
Games
Practise this topic with interactive games.
Games coming soon.
Frequently Asked Questions
What does correlation mean?
A relationship between two variables.
What is positive correlation?
As one increases, the other increases.
What is a line of best fit?
A line showing the trend of the data.