Statistics
Grade 4-6Scatter Graphs & Correlation
A scatter graph plots two variables against each other to show whether they are linked, and exam questions test whether you can describe the correlation, use a line of best fit to estimate values, spot an outlier, and explain why a correlation does not always mean one variable causes the other. This lesson covers all of these skills.
What you need to know
- Scatter graphs show whether two variables are correlated.
- Positive correlation means both rise together; negative means one rises as the other falls.
- A line of best fit follows the trend with roughly equal points either side.
- Correlation does not prove that one variable causes the other.
Written by Asad, co-founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Describing correlation
Positive correlation means both variables increase together, negative correlation means one increases as the other decreases, and no correlation means there is no clear pattern between the two variables.
A scatter graph of hours studied against test score, where the points trend upward from left to right, shows positive correlation.
Reading values and using a line of best fit
To read a value directly, find the known value on one axis and trace across to the nearest point. When a line of best fit is drawn, use the line itself rather than an individual point, since it represents the overall trend more reliably.
A line of best fit for hours revised against exam score passes through roughly (0, 40) and (10, 90). At 6 hours revised, tracing up to the line and across gives an estimated exam score of 70.
Identifying an outlier
An outlier is a point that does not fit the overall trend shown by the rest of the data, sitting noticeably away from the pattern the other points follow.
In a data set showing an otherwise steady positive trend, a point far above where the trend would predict, such as (2, 95), is an outlier.
Correlation versus causation
A strong correlation between two variables does not necessarily mean that one causes the other. Sometimes both variables are affected by an underlying third factor, so the link may be coincidental or indirect rather than a direct cause and effect.
Ice cream sales and drownings both increase in hot weather, so they show a strong positive correlation, but eating ice cream does not cause drowning. Hot weather is the third factor causing both.
Worked examples
Three exam-style questions, fully solved
The scatter graph shows the number of hours studied and the test scores of 10 students, with the points trending upward from left to right. Describe the correlation shown.
Easy- 1.Look at the overall trend of the points: as hours studied increases, test score also increases
Answer: Positive correlation
The scatter graph shows the number of hours revised and exam scores, with a line of best fit drawn passing through roughly (0, 40) and (10, 90). Use the line of best fit to estimate the exam score for a student who revises for 6 hours.
Medium- 1.Find 6 hours on the horizontal axis and trace up to the line of best fit
- 2.Trace across to the vertical axis to read the estimated score
Answer: 70
A scatter graph shows a strong positive correlation between the number of ice creams sold and the number of drownings at a beach resort over a year. Does this mean that eating ice cream causes drowning? Explain your answer.
Hard- 1.Consider whether a direct cause and effect link is plausible: eating ice cream has no physical mechanism that would cause drowning
- 2.Identify the more likely explanation: both ice cream sales and drownings increase in hot weather, since more people swim and buy ice cream when it is hot
Answer: No, both are caused by hot weather, a third factor. Correlation does not imply causation.
Practice
6 questions, marked instantly
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Practice
Now try these yourself.
Type your answer and check it. The worked solution appears once you have had a go.
As the temperature increases, ice cream sales increase. What type of correlation is this?
As a car gets older, its value decreases. What type of correlation is this?
A scatter graph of shoe size against exam score shows points with no clear pattern. What type of correlation is this?
A line of best fit has the equation y = 2x + 5. Use it to estimate y when x = 10.
On a scatter graph, a point that does not fit the pattern of the others is called what?
A line of best fit passes through (0, 3) and (4, 11). Work out its gradient.
Avoid these
The mistakes students make most often
Confusing positive and negative correlation, or describing a scattered graph with no clear pattern as having a correlation.
Reading a value from an individual data point instead of using the line of best fit, when one has been drawn, since the line represents the overall trend more reliably.
Extrapolating using a line of best fit far beyond the range of the plotted data, when the trend may not continue outside that range.
Including the outlier when judging the overall trend or line of best fit, which distorts the pattern shown by the majority of the data.
Assuming a strong correlation between two variables always means one directly causes the other, without considering a third underlying factor.
FAQ
Questions students and parents ask
Before this topic, make sure you know
What to learn next
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