Uncertainty

The uncertainty of a measurement is a way of telling us how precise that measurement is.

It basically says ‘how far off could our measurement be from the actual value?‘

Representing uncertainty

We can represent uncertainty in two main ways:

• Absolute uncertainty
• Percentage uncertainty

Absolute uncertainty

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

Absolute uncertainty can be written like this:

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

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

• Range:
• Absolute uncertainty:
• Absolute uncertainty =

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

• Mean =
• Measurement with uncertainty =

Percentage uncertainty

Percentage uncertainty basically tells us ‘what percentage of the measurement could we be off by?’

For example, if we have a measurement of , that means we could be off by . To find the percentage uncertainty, we can use the formula:

For example, to find the percentage uncertainty of our absolute uncertainty example above ():