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Physics · 1. Measurement and data

Measurement, graphs and uncertainty

Learn repeats, data processing, graphs and reliability before tackling other investigations.

40 minutesContent version: 2.1
Start the interactive pathwayOpen the virtual experiment

Driving question

How do we know a measurement is reliable rather than merely close to an expected value?

Curriculum coverage

Vietnam 2018 scientific enquiry; IGCSE Physics language of measurement and practical skills.

Model scope and limitations

The model focuses on repeats and a T²–L graph; it is not a full university uncertainty analysis.

Learning objectives

  • Distinguish resolution, random error and systematic error.
  • Calculate a mean, range and simple percentage uncertainty.
  • Choose axes, units, a best-fit line and a valid gradient.

Prerequisite knowledge

  • SI conversions and ratios.
  • Reading scales and stopwatches.

Core knowledge

Accuracy and precision

Accuracy is closeness to the accepted value; precision is agreement among repeated readings.

Time many periods

Timing 10–20 periods and dividing reduces the fractional effect of reaction time.

Linearisation

Since T = 2π√(L/g), T² = (4π²/g)L and the gradient gives g.

Worked example

For 10 periods, readings are 20.1 s, 20.3 s and 20.2 s. The mean is 20.2 s, so T = 2.02 s. Half-range is 0.1 s for 10T, or about 0.01 s for T.

Misconceptions to avoid

  • More decimal places do not automatically make a result more accurate.
  • Do not join dots point-to-point; use a best-fit line for the trend.

Virtual experiment procedure: Pendulum measurement of gravitational acceleration

  1. Choose at least five evenly spaced lengths L and keep amplitude small.
  2. For each L, time 10 periods three times and calculate mean T.
  3. Plot T² against L and use two distant points on the best-fit line for the gradient.

Safety and cautions

  • In a real lab, secure the stand and keep the swing area clear.

Evidence to collect

  • A table with L, three 10T readings, mean T and T² with units.
  • A note about any anomaly and whether to repeat or retain it.
Open the virtual experiment
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Diagnostic check

1. Three close readings all displaced from the accepted value suggest what?

  1. Systematic error
  2. Random error only
  3. No error
Show answer and explanation

Correct answer: Systematic error

High precision can coexist with systematic error.

2. Which quantity belongs on the x-axis when length L is deliberately changed?

  1. L
  2. T²
  3. g
Show answer and explanation

Correct answer: L

The independent variable normally goes on the x-axis.

3. Why time 10 periods rather than one?

  1. Reduce fractional reaction-time error
  2. Increase g
  3. Remove all systematic error
Show answer and explanation

Correct answer: Reduce fractional reaction-time error

The same timing error is a smaller fraction of a longer interval.

Application practice

1. What is the mean of 4.8, 5.0 and 5.2 s?

  1. 5.0 s
  2. 4.9 s
  3. 5.2 s
Show answer and explanation

Correct answer: 5.0 s

(4.8 + 5.0 + 5.2)/3 = 5.0 s.

2. A T²–L graph has gradient 4.02 s²/m. Approximate g using g = 4π²/gradient.

  1. 9.82 m/s²
  2. 4.02 m/s²
  3. 39.5 m/s²
Show answer and explanation

Correct answer: 9.82 m/s²

4π²/4.02 ≈ 9.82 m/s².

3. What is the best response to a point far from the trend?

  1. Check and repeat before deciding
  2. Delete it immediately
  3. Bend the line through it
Show answer and explanation

Correct answer: Check and repeat before deciding

Anomalies should be investigated, not automatically deleted.

Academic references

  1. Cambridge IGCSE Physics 0625 — official syllabus and resources
  2. Cambridge AS & A Level Physics 9702 — official syllabus
  3. OpenStax Physics — peer-reviewed high-school physics
  4. BIPM — SI Brochure, 9th edition

This lesson is maintained against the cited sources below. Simulations are learning models and do not replace supervised physical-laboratory safety procedures.

Content publisher
WebLab STEM
Technical maintainer
Đức Tiến — Control & Automation Engineer