Lesson 10.3 · 25 min
Scatter Graphs and Correlation
Plotting pairs of data, describing correlation, drawing a line of best fit and using it to estimate.
In this lesson you will learn to…
- Plot a scatter graph from paired data
- Describe correlation as positive, negative or none, and strong or weak
- Interpret correlation in the context of the data
- Draw a line of best fit and use it to estimate values; spot outliers
Why this matters
Scientists use scatter graphs to look for relationships: does more exercise lead to more weight loss? Does a city’s height above sea level affect the temperature water boils at? A scatter graph shows at a glance whether there is a link and how strong it is.
Types of correlation
| Pattern | Name | Example |
|---|---|---|
| Points rise from left to right | positive | height and arm length |
| Points fall from left to right | negative | height above sea level and boiling point |
| No pattern | none | maths score and hair length |
Making predictions
Read up from the -axis to your line of best fit, then across to the -axis. This is reliable within the range of your data. Going beyond it — predicting the earnings of a 90-year-old from data on 25–57 year-olds — is risky, because the trend may not continue.
Be careful with small samples
Habibah plotted five friends’ arm lengths against hours of TV watched and saw a positive correlation. Layla is right to be sceptical: five points is far too few, and there is no sensible reason why arm length would affect TV watching. A pattern in a tiny sample can easily be a coincidence.
Key rules and formulas
Describe the correlation
Positive: as one variable increases, so does the other. Negative: as one increases, the other decreases. None: no pattern at all. Strong means the points lie close to a straight line; weak means they are scattered.Interpret it
Describing says "strong positive correlation". Interpreting says what it means: "as height increases, mass increases".Line of best fit
A straight line that follows the trend, passes close to as many points as possible and has roughly as many points above it as below. It does not have to go through the origin.Correlation is not causation
Two variables can be correlated without one causing the other — ice-cream sales and sunburn both rise in summer, but ice cream does not cause sunburn.
Worked examples
Using a line of best fit
Try it yourself first, then reveal the solution one step at a time.
Spotting an outlier
Try it yourself first, then reveal the solution one step at a time.
Practice: scatter graphs and correlation
9 questions
Question 1 of 9Match the pairsFoundation Match each pair of variables to the correlation you would expect.Pick an answer, then choose the row it belongs to. You can also drag it.
- Height and arm length
- Height above sea level and boiling point of water
- A person's mass and their history test score
- Size of car and fuel economy (km per litre)
Question 2 of 9Click the diagram Time taken to write a name backwards against its number of letters. Click the outlier.Click the right part of the diagram. You can also tab to each part and press Enter.
Question 3 of 9Choose all that apply Select every true statement about lines of best fit.Select every correct answer — there may be more than one.
Question 4 of 9Type the answer A line of best fit for age against yearly earnings passes through and . Estimate the earnings of a 48-year-old, to the nearest thousand dollars.dollarsQuestion 5 of 9Type the answer Using the same line, estimate the age of someone earning 23 000 dollars a year.yearsQuestion 6 of 9Multiple choice Height above sea level (m) and boiling point (°C): (1000, 96), (1600, 94), (2200, 92), (3600, 88), (4800, 84), (6400, 78), (7200, 76). Estimate the boiling point at 3000 m.Question 7 of 9Click the diagram Book pages against mass (g). Which point is the heaviest book? Click it.Click the right part of the diagram. You can also tab to each part and press Enter.
Question 8 of 9True or false If two variables show a strong positive correlation, an increase in one must cause an increase in the other.Question 9 of 9Multiple choice Habibah plots arm length against hours of TV for five friends and sees a positive correlation. What is the best response?