Graphs and Evaluation

A good graph has labelled axes with units, scales that use more than half the grid, plotted points marked clearly and a thin best-fit line with points balanced on both sides. For the gradient, use a large triangle covering at least half the line and read its corners from the line, not from data points. Compare the gradient and intercept with a theoretical equation to find constants. Evaluating means identifying the biggest sources of uncertainty and suggesting specific, practical improvements.

Cambridge 9702 Paper 3Edexcel YPH11 WPH13Edexcel YPH11 WPH16AQA 7408 Paper 3A≈ 35 minRevision 6 · updated 2026-10-27

Section 1 of 14

Learning objectives

Choose scales and plot points accurately.
Draw best-fit lines and calculate gradients and intercepts.
Relate gradient and intercept to an equation of the form $y=mx+c$ .
Identify sources of uncertainty and suggest specific improvements.

Pause and think

Your graph's best-fit line misses one point by a mile. Should you force the line through it?

Section 2 of 14

Core idea

Start hereHow uncertain is a gradient?

A best-fit line gives one gradient, but the points could be fitted by slightly steeper or shallower lines too. The steepest or shallowest line that still passes through every error bar shows how uncertain your result is.

The big idea

Error bars; best-fit line; worst acceptable line. Gradient uncertainty = |best − worst|.

1. Best and worst lines

Best fit and worst acceptable lines with error bars

For a pendulum

T^2=\dfrac{4\pi^2}{g}l

: gradient

\dfrac{4\pi^2}{g}=4.03

gives

g=9.80

m s

^{-2}

. Uncertainty in gradient

=|4.40-4.03|=0.37

Linearising

T=2\pi\sqrt{\frac lg}

$T^2=\frac{4\pi^2}g\,l$
Square both sides.
$\text{gradient}=\frac{4\pi^2}g\Rightarrow g=\frac{4\pi^2}{\text{gradient}}$
Plot $T^2$ against $l$ .

Worked examplePendulum results

Best gradient 4.03 s² m $^{-1}$ ; worst 4.40.

Goal: $g$ with uncertainty.
Strategy: Percentage uncertainty carries through.

$\Delta m=4.40-4.03=0.37$
Gradient uncertainty.
$g=\frac{4\pi^2}{4.03}=9.80$
From the best line.
$\frac{0.37}{4.03}=9\%\Rightarrow\pm0.9$
Same percentage for $g$ .

Answer

g=9.8\pm0.9

m s

^{-2}

✓ CheckAccepted 9.81 inside the range ✓.

Points fill more than half the grid.
Gradient triangle at least half the line.
Read coordinates from the line.

Common misconceptionData points in the triangle Use points on the drawn line, not table values.

Summary

Error bars, best fit, worst line.

Worst acceptable line: Steepest or shallowest line through all error bars.

HistoryGalileo's inclined planes. Galileo measured balls rolling down ramps using a water clock, weighing water collected during each roll. He found distance proportional to time squared, one of the first relationships found by systematically varying one quantity and measuring another.

Fun factThe "fudge factor" problem. Scientists have been caught drawing lines that fit their expectations rather than their data. Modern labs often use software to fit lines objectively, but the human skill of judging a best fit is still examined, because you need to spot when the software's fit doesn't make sense.

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