Uncertainties
Precision
- Precise measurements are ones in which there is very little spread about the mean value, in other words, how close the measured values are to each other
- If a measurement is repeated several times, it can be described as precise when the values are very similar to, or the same as, each other
- Another way to describe this concept is if the random uncertainty of a measurement is small, then that measurement can be said to be precise
- The precision of a measurement is reflected in the values recorded – measurements to a greater number of decimal places are said to be more precise than those to a whole number
Accuracy
- A measurement is considered accurate if it is close to the true value
- Another way to describe this concept is if the systematic error of a measurement is small, then that measurement can be said to be accurate
- The accuracy can be increased by repeating measurements and finding a mean of the results
- Repeating measurements also helps to identify anomalies that can be omitted from the final results
The difference between precise and accurate results
Representing precision and accuracy on a graph
Types of Uncertainty
- There is always a degree of uncertainty when measurements are taken; the uncertainty can be thought of as the difference between the actual reading taken (caused by the equipment or techniques used) and the true value
- Uncertainties are not the same as errors
- Errors can be thought of as issues with equipment or methodology that cause a reading to be different from the true value
- The uncertainty is a range of values around a measurement within which the true value is expected to lie, and is an estimate
- For example, if the true value of the mass of a box is 950 g, but a systematic error with a balance gives an actual reading of 952 g, the uncertainty is ±2 g
- These uncertainties can be represented in a number of ways:
- Absolute Uncertainty: where uncertainty is given as a fixed quantity
- Fractional Uncertainty: where uncertainty is given as a fraction of the measurement
- Percentage Uncertainty: where uncertainty is given as a percentage of the measurement
- To find uncertainties in different situations:
- The uncertainty in a reading: ± half the smallest division
- The uncertainty in repeated data: half the range i.e. ± ½ (largest - smallest value)
- The uncertainty in digital readings: ± the last significant digit unless otherwise quoted
How to calculate absolute, fractional and percentage uncertainty
- Always make sure your absolute or percentage uncertainty is to the same number of significant figures as the reading