Line of best fit (Edexcel GCSE Statistics): Revision Notes
Line of best fit
What is a line of best fit?
A line of best fit is a straight line drawn through data points on a scatter diagram that best represents the overall trend or relationship between two variables. This line allows you to summarise the relationship shown in your data and make predictions about values that weren't directly measured.
The key purpose of a line of best fit is to help you predict unknown values. For example, if you know one variable's value, you can use the line to estimate what the other variable might be.
How to draw a line of best fit
When drawing a line of best fit, you need to follow several important rules to ensure it accurately represents your data:
Key rules for drawing the line
The line must pass through the mean point. This is the most crucial requirement. The mean point is calculated using the coordinates , where represents the mean of all x-values and represents the mean of all y-values.
Extend the line beyond your data. Your line should stretch before the first data point and after the last data point, ensuring it covers the full range where you might want to make predictions.
Balance the points. Try to have roughly equal numbers of data points above and below your line. The line doesn't need to pass through every single point, but should represent the overall trend.
The line doesn't need to pass through the origin (0,0). Unlike some other types of graphs, your line of best fit should follow the data trend, not force itself through the origin.
Calculating the mean point
The mean point is found using these formulas:
Where:
- means the sum of all x-values multiplied by their frequencies
- means the sum of all y-values multiplied by their frequencies
- means the sum of all frequencies
If you're working with simple data without frequencies, these formulas simplify to just finding the mean of your x-values and the mean of your y-values separately.
Making predictions using the line of best fit
Once you've drawn your line of best fit, you can use it to make predictions by reading values directly from the graph.
Steps for making predictions
- Find your known value on the appropriate axis (either x or y)
- Draw a vertical or horizontal line from this point until it meets your line of best fit
- Read off the corresponding value on the other axis
- Remember this is an estimate, not an exact answer
Worked example: Car prices and age
Worked Example: Predicting Car Price from Age
Given information: A scatter diagram shows car prices (£) against their ages (years). The mean point is at (4, 4600), meaning the average age is 4 years and the average price is £4600.
Task: Predict the price of a car that is 5.5 years old.
Step-by-step solution:
- Draw the line of best fit passing through the mean point (4, 4600) and extending it to cover all the data range
- Locate 5.5 years on the x-axis (the age axis)
- Draw a vertical line upwards from 5.5 years until it intersects the line of best fit
- Draw a horizontal line across from this intersection point to the y-axis (price axis)
- Read the price value where the horizontal line meets the y-axis
Answer: The predicted price is approximately £3400.
This example shows how the line of best fit allows you to estimate values that weren't directly measured in your original data set.
Important exam tips
Watch out for these common mistakes:
- Forgetting to pass the line through the mean point
- Not extending the line far enough beyond the data points
- Trying to pass the line through every single data point instead of showing the general trend
- Confusing which axis represents which variable when making predictions
Remember to:
- Always show your working when making predictions
- Label your axes clearly
- State that your answer is an estimate or prediction
- Check that your line looks reasonable compared to the data trend
Summary
Key Points to Remember:
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A line of best fit summarises the relationship between two variables and helps you make predictions about unknown values
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The line must pass through the mean point , which you calculate using the mean of your x-values and y-values
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Extend your line beyond the data points so it covers the full range where you might need to make predictions
-
To make predictions, read values directly from the line by drawing vertical and horizontal lines to the axes
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Your predictions are estimates, not exact values, so always describe them as such in your answers