Uncertainty

Uncertainty definition

Measure of spread of values which is likely to include the ‘true value’

Absolute uncertainty in analogue and digital readings

Analogue: Half the instrument’s resolution (e.g. if measuring temperature with a mercury thermometer: (300 +- 0.5 K))

Digital: Uncertainty in readings are assumed to be the last significant digit

Uncertainties in calculated values

1. Adding and subtracting values → Add absolute uncertainties
2. Multiplying and dividing values → Add percentage uncertainties
3. Raising values to a power → Multiply percentage uncertainties by the power

Quoting uncertainties with data

Uncertainity in any numerical data should be quoted to 1 significant figure; the data itself should then be corrected to the same number of decimal places as the uncertainty

Graphing data with uncertainties

1. Plot the data at the mean value
2. Calculate the range of data, ignoring any anomalies


1. Add error bars with lengths equal to half th range on either side of the data point

Uncertainties in gradient and intercept of a straight-line graph

Draw steepest and shallowest possible line of best fit, passing through most of the erros bars. The gradient of each line should then be found.

\
%Uncertainty = |best gradient - worst gradient|/|best gradient| \* 100%