Errors and Uncertainty in Measurements

All measurements contain some degree of uncertainty. Understanding errors helps you evaluate the reliability of experimental results.

Systematic errors

Systematic errors affect all readings by the same amount in the same direction. They shift all results consistently high or consistently low.

Causes: zero error on an instrument, incorrectly calibrated scale, reaction time in manual timing.

Systematic errors cannot be reduced by repeating measurements. They require recalibration or a change in method.

Random errors

Random errors cause readings to scatter above and below the true value. They vary unpredictably between measurements.

Causes: parallax when reading a scale, fluctuations in environmental conditions, slight variations in experimental technique.

Random errors can be reduced by taking multiple readings and calculating the mean.

Precision vs accuracy

• Precise: readings are close to each other (small spread).
• Accurate: readings are close to the true value.

A set of readings can be precise but not accurate (systematic error shifts them all). Accurate results require both good precision AND no systematic error.

Estimating uncertainty

For a single reading, the uncertainty is usually $\pm$ half the smallest division.

For repeated readings, the uncertainty can be estimated as half the range:

$\text{uncertainty} = \frac{\text{max} - \text{min}}{2}$

Common errors and how to correct them

• Confusing precision with accuracy.
• Thinking that repeating measurements removes systematic errors (it only reduces random errors).

How to apply this in an exam

Identify whether an error is systematic or random. State how each type affects results and how to reduce it. Give specific examples relevant to the experiment described.