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LearnYPH11WPH16 · Unit 6: Practical Skills in Physics IIPractical skillsAnalysis, error bars and evaluation
Practical skills · Subtopic 4 of 4

Analysis, Error Bars and Evaluation

In Paper 5's analysis question, you calculate derived values (like lg⁡x\lg x, 1x\dfrac1x or x2x^2) with their uncertainties, plot them with error bars, then draw the best-fit line and a worst acceptable line that still passes through all error bars. The uncertainty in the gradient is the difference between their gradients; similarly for the intercept. Use these to find a constant with its uncertainty, and say whether the data support the hypothesis.

Cambridge 9702 Paper 5Edexcel YPH11 WPH16AQA 7408 Paper 3A≈ 40 minRevision 5 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Find uncertainties in derived quantities, including logarithms.
  • Plot error bars and draw best-fit and worst acceptable lines.
  • Find the uncertainty in a gradient and intercept.
  • Calculate constants with uncertainties and draw conclusions.
Pause and think

Your best-fit line gives g=9.6g=9.6 m s⁻² and your worst acceptable line gives g=10.1g=10.1 m s⁻². What's your final answer?

Section 2 of 14

Core idea

Start hereClose enough?

Your graph's line misses the origin by a little. Is that a real effect, or just measurement error? The only honest way to decide is to compare the miss with your uncertainty.

The big idea

Compare data with prediction including uncertainties. Proportional: straight line through the origin within uncertainty. Evaluate with specific errors and improvements.

1. Testing proportionality

Does the data support y ∝ x? Check the line passes through the origin within uncertainty
123456246810120xybest fit: intercept 0.6through origin?
The best-fit intercept is 0.6 ± 0.3: zero is outside the range, suggesting a systematic error (e.g. a zero error) or that yy is not simply proportional to xx.
Worked exampleIntercept 0.6 ± 0.3

Is y∝xy\propto x?

Goal
Decision.
Strategy
Does the range include 0?
  1. 0.3≤c≤0.90.3\le c\le0.9
    Range of the intercept.
  2. 0∉[0.3,0.9]0\notin[0.3,0.9]
    Excludes zero.
AnswerNot proportional, or a systematic (zero) error.
✓ CheckWith ±0.7 the conclusion would flip ✓.
Worked exampleConstant ratio

k=y/xk=y/x from two readings: 2.10 and 2.25; estimated uncertainty ~10%.

Goal
Supported?
Strategy
Percentage difference vs uncertainty.
  1. 0.152.18=7%\frac{0.15}{2.18}=7\%
    Difference ÷ mean.
  2. 7%<10%7\%<10\%
    Within uncertainty.
AnswerData support y∝xy\propto x.
✓ CheckA 15% difference would not ✓.

2. Evaluating

  • Sources of error specific to this experiment.
  • Specific improvements ("use light gates", not "be more careful").
Common misconception"Repeat the experiment" On its own it doesn't fix systematic errors: say what and how.

Summary

  • Compare with uncertainty.
  • Specific errors and improvements.
Key words
Systematic error
Consistent offset in readings.
HistoryMillikan's "best" drops. Robert Millikan's oil-drop measurement of the electron's charge was slightly too low because of an error in air viscosity. Later experimenters crept towards the right value slowly, partly because they doubted results far from Millikan's. Honest uncertainty estimates help avoid this kind of bias.
Fun factFaster-than-light neutrinos. In 20112011 the OPERA experiment reported neutrinos arriving 6060 nanoseconds early, apparently faster than light. The physicists published, asking for checks. The cause was a loose fibre-optic cable: a systematic error no error bar would show.
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