Scatter Graphs and Line of Best Fit
A scatter graph plots pairs of values for two related variables as points on a coordinate grid, so that any pattern or relationship (correlation) between them can be seen. In GCSE Statistics, a line of best fit is a straight line drawn through the middle of the points on a scatter graph, used to describe and estimate values for the relationship between the two variables.
Method
- Plot each pair of values as a single point on a coordinate grid, with one variable on the horizontal axis and the other on the vertical axis.
- Look at the overall pattern of the points to decide whether there is positive, negative or no correlation.
- If the points show a roughly linear pattern, draw a single straight line of best fit that passes as close as possible to all the points, with a similar number of points on each side.
- The line of best fit does not have to pass through the origin or through any particular point, unless the data specifically supports this.
- Use the line of best fit to estimate an unknown value by reading up or across from a known value to the line, then across or down to the other axis.
- Be cautious about extrapolating, estimating far beyond the range of the plotted data, since the relationship may not continue in the same way.
Worked example
A scatter graph plots the number of hours revised against the test score for 10 students. A line of best fit is drawn. A student who revised for 5 hours reads across to the line of best fit at a test score of 62, and a student who revised for 8 hours reads across to the line of best fit at a test score of 80. Use these two points on the line to estimate the test score for a student who revises for 6.5 hours.
- Find how much the score increases for each extra hour of revision along the line: (80 - 62)/(8 - 5) = 18/3 = 6 marks per hour.
- Find the difference in hours between the student we want and the known point at 5 hours: 6.5 - 5 = 1.5 hours.
- Multiply the increase per hour by this difference: 1.5 x 6 = 9 marks.
- Add this to the score at 5 hours: 62 + 9 = 71.
- Final answer: the estimated test score for 6.5 hours of revision is 71.
Practice questions
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Q1A scatter graph shows points that generally rise from bottom left to top right. What type of correlation does this show?Show answer
Answer: Positive correlation.
Q2A scatter graph shows points that generally fall from top left to bottom right. What type of correlation does this show?Show answer
Answer: Negative correlation.
Q3A scatter graph shows points scattered with no clear pattern. What type of correlation does this show?Show answer
Answer: No correlation (zero correlation).
Q4A line of best fit passes through the points (0, 4) and (10, 24). Find its gradient.Show answer
Answer: 2 (rise/run = (24-4)/(10-0) = 20/10 = 2).
Q5Using the line of best fit from the previous question, estimate the y-value when x = 6.Show answer
Answer: 16 (y = 4 + 2 x 6 = 16, using the gradient of 2 and starting value of 4 at x = 0).
Q6Explain why estimating a y-value for x = 50 would be unreliable if all the plotted data only covers x-values from 0 to 20.Show answer
Answer: This would be extrapolation, estimating far outside the range of the collected data, where the relationship might not continue in the same pattern.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A scatter graph plots the age of a car, in years, against its value, in pounds. Describe the type of correlation you would expect to see, and explain your reasoning.
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A scatter graph shows the number of ice creams sold plotted against the daily temperature, in degrees C, for 12 days. A line of best fit is drawn. On the line, a temperature of 20 degrees C corresponds to 45 ice creams sold, and a temperature of 30 degrees C corresponds to 85 ice creams sold. Use the line of best fit to estimate the number of ice creams sold when the temperature is 25 degrees C.
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A student says: 'My scatter graph shows a strong positive correlation between the number of pet cats owned in a town and the number of trees in that town, so owning more cats must cause more trees to grow.' Explain why the student's conclusion is not justified.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
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This topic is chapter 12 of GCSE Statistics Foundation Workbook 2 and chapter 17 of GCSE Statistics Higher Workbook 2, the whole course as one free printable PDF.
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