2.2.1Foundations in Physics
Sources of Uncertainty
5 min read 5 parts Lesson 15 of 19 Unit quiz Virtual lab
Section 1 of 5Types of Error
Every measurement differs from the true value by some uncertainty, which comes from errors of two kinds.
Random error
- Causes readings to scatter unpredictably above and below the true value, so it affects precision.
Systematic error
- Shifts all readings in the same direction by the same amount, so it affects accuracy.
Zero error
- A systematic error where an instrument gives a non-zero reading at zero;
- it must be subtracted from every reading.
Parallax
- Reading a scale from the wrong angle makes values consistently too high or too low.
Reaction time
- A human delay when starting and stopping a timer is a source of random error and uncertainty.
Section 2 of 5Describing Measurements
Describing Measurements
Precision
- How closely repeated readings agree with each other, which is reduced by random error.
Accuracy
- How close a reading is to the true value, which is reduced by systematic error.
Resolution
- The smallest change an instrument can show, such as 1 mm on a ruler or 0.01 V on a digital meter.
Repeatability
- Getting the same results when the same person repeats the experiment under the same conditions.
Reproducibility
- Getting the same results when different people or methods are used, which shows the result is robust.
Section 3 of 5Estimating Uncertainty
1
For a single reading, the uncertainty is usually taken as plus or minus half the smallest scale division.
2
For a digital instrument, the uncertainty is normally the smallest digit displayed.
3
For repeated readings, find the mean and use half the range as the uncertainty in that mean.
4
Averaging many readings reduces the effect of random errors but cannot remove a systematic error.
5
Improve a measurement by using an instrument with finer resolution, or by measuring a larger quantity.
Section 4 of 5Worked Example
Question
- Five measurements of the period of a pendulum are 1.52 s, 1.48 s, 1.50 s, 1.55 s and 1.45 s.
- Find the mean period and its uncertainty using half the range.
- Mean = (1.52 + 1.48 + 1.50 + 1.55 + 1.45) ÷ 5 = 7.50 ÷ 5 = 1.50 s.
- Range = 1.55 − 1.45 = 0.10 s.
- Uncertainty = half the range = 0.05 s.
Answer The period is 1.50 ± 0.05 s.
Section 5 of 5Exam Checklist & Tips
2.2.1 – Key Points for the Exam
- Uncertainty An estimate of the range within which the true value of a measurement is expected to lie.
- Random error An unpredictable variation in readings that affects precision.
- Systematic error A consistent offset in readings that affects accuracy.
- Precision The closeness of agreement between repeated measurements.
- Accuracy The closeness of a measurement to the true value.
Common Mistakes
- Saying that averaging repeated readings removes a systematic error.
- Confusing precision with accuracy; a set of readings can be precise but inaccurate.
- Using the resolution of the instrument as the whole uncertainty when readings vary more than that.
- Treating a human blunder as an uncertainty rather than discarding or repeating the reading.