How can you calculate uncertainty in measurements?

Uncertainty in measurements can be calculated by determining the range of possible values and expressing it as ± value.

In more detail, uncertainty is a way of quantifying the doubt about the measurement result. Every time we make a measurement in a scientific experiment, there is always a degree of uncertainty associated with it. This is because all measurements are subject to some degree of error or uncertainty, and it is important to recognise this when analysing results.

There are two types of uncertainties in measurements: random and systematic. Random uncertainties are caused by unpredictable statistical variations and can be reduced by taking the average of a large number of observations. Systematic uncertainties, on the other hand, are predictable and typically constant or proportional to the true value. These are often due to faults in the measurement instrument or the method of observation.

To calculate the uncertainty in a measurement, you first need to identify the type of uncertainty. For random uncertainties, you can calculate the standard deviation of your measurements. This is a measure of how spread out your data is from the mean. The standard deviation can be calculated using a statistical formula, which involves subtracting the mean from each data point, squaring the result, adding these squared values together, dividing by the number of data points minus one, and then taking the square root.

For systematic uncertainties, you can estimate the uncertainty based on the precision of the instrument. For example, if you are using a ruler with millimetre marks, the uncertainty is ± 0.5 mm because you have to estimate the last digit.

Once you have calculated the uncertainty, it is usually expressed as a ± value. For example, if you measure the length of a table as 2.00 m with an uncertainty of 0.01 m, you would report the measurement as 2.00 ± 0.01 m. This means that the true length of the table is likely to be between 1.99 m and 2.01 m.

Remember, it's important to consider uncertainty in your measurements as it gives a range of values that could be the true value. It's a crucial part of scientific measurement and analysis.