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Scatter graphs

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Summary

Scatter graphs

​​In a nutshell

A scatter graph is a graph displaying plotted data points.  The graph tells you how closely variables are related to each other as well as the kind of relation they have. 



Interpreting scatter graphs

Scatter graphs tell you about correlation between variables. They do not prove that one variable has an effect on another - correlation could happen because of a third factor or just by coincidence.


Definitions

Correlation

How closely two variables are related


Outliers

Points on the graph that do not fit the trend

Maths; Statistics; KS4 Year 10; Scatter graphs

Line of best fit

A straight line drawn through the middle of points, as close to each one as possible

Maths; Statistics; KS4 Year 10; Scatter graphs

Strong correlation

Points make a fairly straight line

Maths; Statistics; KS4 Year 10; Scatter graphs

Weak correlation

Points stray more from a straight line, but there is still positive or negative correlation

Maths; Statistics; KS4 Year 10; Scatter graphs

Negative correlation

Sloping downhill from left to right

Maths; Statistics; KS4 Year 10; Scatter graphs

Positive correlation

Sloping uphill from left to right

Maths; Statistics; KS4 Year 10; Scatter graphs

No correlation

Points have no pattern

Maths; Statistics; KS4 Year 10; Scatter graphs



Making predictions using scatter graphs

By drawing a line of best fit, you can make predictions using scatter graphs. It is important when drawing a line of best fit to ignore any outliers, as these could be potentially caused by an error that occurred during the experiment or when recording the data.


Tip: When drawing a line of best fit, make sure there are the same amount of points above the line as there are below.



Example 1

This scatter graph shows the correlation between the number of books read per year and age.

Maths; Statistics; KS4 Year 10; Scatter graphs


Draw a line of best fit and predict how many books per year a thirty-five year old would read.

Maths; Statistics; KS4 Year 10; Scatter graphs

Reading up and along, you can predict that a thirty-five year old would read 16\underline {16 } books a year.


Note: In the example above, the line of best fit has been 'extrapolated' to make a prediction about the future.



Accuracy of predictions

Extrapolation

A type of estimation which goes outside the original range of observed or recorded values, based on the trends in the previous results.


Whilst this does provide a useful prediction, it is not always reliable as you have no way of knowing whether the current trend in data will remain the same.




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Exercises

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FAQs - Frequently Asked Questions

What is weak correlation?

What is strong correlation?

What is a line of best fit?

What is an outlier point?

What is a scatter graph?

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