1.3 Errors and uncertainties

A systematic error shifts readings in a consistent direction, while random error causes scatter between repeated readings. A zero error is a systematic offset from a faulty zero.

Repeat measurements and average to reduce random variation; calibration, zero checks or a changed method address systematic bias. Repeats cannot remove a constant offset.

A balance reading 0.20 g with an empty pan adds 0.20 g to every mass unless corrected.

A precise cluster can still be inaccurate if it is systematically shifted.

Precision is the agreement among repeated measurements; accuracy is closeness to an accepted or true value. A result may be precise but inaccurate, or accurate on average but imprecise.

Use repeated readings to assess spread and a reference value or calibration to assess bias. Report uncertainty alongside a measured value.

Readings 10.1,10.1,10.2 are precise; if the true value is 10.8 they are not accurate.

More decimal places do not create accuracy, and averaging removes random scatter but not systematic error.

For addition or subtraction, add absolute uncertainties. For multiplication, division or powers, add fractional or percentage uncertainties multiplied by the relevant power.

Keep units consistent, avoid overstating precision and round the uncertainty to an appropriate significant figure before matching the value’s decimal place.

For L=2.0±0.1 m and W=3.0±0.1 m, perimeter 2L+2W has absolute uncertainty 2(0.1)+2(0.1)=0.4 m.

Adding percentage uncertainties to an addition is wrong; the operation determines which uncertainty form is appropriate.