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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

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. OpenStax Physics — peer-reviewed high-school physics
  2. 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