Absolute uncertainty

To calculate the absolute uncertainty of a set of measurements, we can use the formula:

\text{absolute uncertainty} = \frac{\text{range}}{2}

Absolute uncertainty can be written like this:

\text{mean} \pm \text{absolute uncertainty}

For example, 5.0cm \pm 0.1cm means the actual value could be anywhere between 4.9cm and 5.1cm (0.1cm above or below 5.0cm).

Find the absolute uncertainty of the measurements 5.1cm, 5.3cm, 5.2cm, and 5.4cm

• range: 5.4cm - 5.1cm = 0.3cm
• Absolute uncertainty: \frac{0.3cm}{2} = 0.15cm
• Absolute uncertainty = \pm0.15cm

If we wanted to express it with the average measurement, we would do:

• mean = (5.1cm + 5.3cm + 5.2cm + 5.4cm)\div4 = 5.25cm
• Measurement with uncertainty = 5.25cm \pm 0.15cm