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Cambridge IGCSE Mathematics — 0580 Extended

Topic 9.6: Statistics — Scatter Diagrams

Two quantitative variables, plotted as small crosses (\(\times\)). Correlation is the word for the trend: positive, negative, or zero. A line of best fit is one ruled line, drawn by eye across the full data set, with a roughly even spread of points either side.

Types of correlation

Positive: as \(x\) increases, \(y\) tends to increase. Negative: \(y\) tends to decrease. Zero: no trend — do not force a line through a shapeless cloud.

Hours revised versus test mark with positive correlation and a rising line of best fit
Marks tend to rise with hours. The crosses are ×, not dots.
Two scatter graphs: negative correlation and zero correlation
Zero correlation: leave the line off the paper.

Line of best fit

One ruled line, across the whole cloud, not a join-the-dots. It does not need to pass through any plotted cross. It should pass close to the centroid (the mean point) and leave points roughly balanced either side over its whole length.

Scatter with line of best fit through the centroid (4.5, 51)
A single ruled line. Missing every plotted cross can still be correct.

Interpolation

Reading from the line inside the data is interpolation. Draw a dashed line up from the given \(x\), across to the axis, and show it on the paper.

Estimate the mark after 3.5 hours of revision.

Dashed read-off from 3.5 hours across the line of best fit to about 46 marks
About 46 marks. Stay between 1 and 8 hours — that is the plotted range.

Extrapolation

Outside the data the trend may not continue. Extended papers expect the word unreliable (or equivalent) as well as any number you read.

Dashed extension of the line of best fit beyond 8 hours, labelled unreliable
12 hours sits off the right of the plotted crosses. Do not treat 90 marks as a fact.

Paper 2 (non-calculator)

Read to the nearest square the graph allows. A mark of “about 46” with construction lines beats a pretend-exact 45.857.

Try this

Why is a mark estimated at 11 hours of revision unreliable?

Show answer
Answer

  1. 11 hours is outside the plotted data (1 to 8 hours). The trend may not continue — this is extrapolation.

Exam Traps

  • Joining the first plotted point to the last is not a line of best fit. The line must balance the whole cloud, not the two extremes.

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