Accuracy, Precision & Error in Measurement

 

Physics relies on measurements—but no measurement is ever perfect. Understanding accuracy, precision, and error is essential for students preparing for IGCSE, CBSE, or any science competition. This guide covers every concept you need, with simple explanations and examples.

What is Measurement?

Measurement is the comparison of an unknown quantity with a standard. Every measurement comes with some uncertainty.

  • Physical Quantity: The property being measured (length, mass, time, etc.)
  • Unit: Standard for comparison (meter, kilogram, second, etc.)
  • Instrument: Device used (ruler, stopwatch, etc.)

Accuracy vs. Precision

Accuracy

Accuracy describes how close a measured value is to the true or accepted value.
Think: Hitting the bullseye.

Precision

Precision describes how close repeated measurements are to each other, regardless of accuracy.
Think: Grouping of arrows, even if not at the bullseye.

Accuracy = closeness to true value, Precision = closeness to each other

What is Error?

Error is the difference between a measured value and the true value. Every measurement has some error, no matter how careful you are.

Types of Errors

  • Systematic Error: Consistent, repeatable error (e.g. faulty instrument, calibration error). Affects accuracy.
    Example: A scale that always reads 5g too high.
  • Random Error: Fluctuates in magnitude and direction; due to unpredictable factors (tiny air currents, reaction time). Affects precision.
    Example: Stopwatch measurements varying each trial.
  • Gross Error: Major mistakes or blunders (wrong reading, instrument misuse).

How to Reduce Errors

  • Use well-calibrated instruments
  • Take multiple measurements and average
  • Careful reading (avoid parallax)
  • Control external factors (temperature, vibration, etc.)

Quantifying Error: Formulas

  • Absolute Error: |Measured Value – True Value|
  • Mean Absolute Error: Σ|Measured Value – Mean Value| / n
  • Relative Error: Absolute Error / True Value
  • Percentage Error: (Absolute Error / True Value) × 100%
  • Standard Deviation: Measure of precision (spread of repeated values).

Examples & Real-Life Applications

  • Accuracy: A digital thermometer correctly reads 37°C when placed in melting ice (0°C).
  • Precision: Weighing a 100g mass repeatedly gives values 99.8g, 99.9g, 99.8g, 99.9g (high precision, but if actual mass is 100g, not perfectly accurate).
  • Error: A stop clock consistently started late, adding 0.2s to every reading (systematic error).

Common Misconceptions

  • High precision does not guarantee accuracy.
  • Zero error is rarely possible—focus on minimizing, not eliminating, error.
  • Systematic errors cannot be reduced by averaging.
  • Errors are not mistakes, but natural uncertainties in measurement.

Practice Questions

  1. If a thermometer reads 98.8°C when the actual temperature is 100°C, what is the absolute and percentage error?
  2. Four measurements of a length are: 7.1 cm, 7.2 cm, 7.0 cm, 7.1 cm. Find the mean, mean absolute error, and comment on precision.
  3. Explain the difference between systematic and random errors with examples from daily life.
  4. Why is it important to repeat measurements in a physics experiment?

Summary

Accuracy, precision, and error are the foundation of reliable science. Remember: accuracy = correctness, precision = consistency, and error = unavoidable uncertainty. Master these for top results in IGCSE, CBSE, NEET, or any physics test!

Your success, our commitment.
Team Hodu Academy

Last modified: Friday, 18 July 2025, 2:53 PM