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Representing data

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# Scatter diagrams

## Line of best fit

The 'line of best fit' goes roughly through the middle of all the scatter points on a graph. The closer the points are to the line of best fit the stronger the correlation is.

### Example

10 pupils in a school study French and German at GCSE. Their marks for a recent test are recorded in the table below:

Name Mark in French Mark in German
Ben 42 48
Sarah 62 56
Sunil 32 24
Tom 78 68
Pete 70 ?
Henry 18 22
Siobhan 68 76
Andrew 52 54
Jo 84 89
Gita 38 39

You can draw a scatter diagram to represent these marks. As Pete was absent on the day of the German test you do not have enough information to mark his score.

Looking at this scatter diagram there is strong positive correlation between the marks in French and the marks in German, so you can draw a line of best fit to show that trend.

Pete scored 70 in French, so using the line of his best fit, you can estimate that his mark in German would have been 72.

A line of best fit can only be drawn if there is strong positive or negative correlation.
The line of best fit does not have to go through the origin.
The line of best fit shows the trend, but it is only approximate and any readings taken from it will be estimations.

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