How does averaging multiple measurements reduce error?

Averaging multiple measurements reduces error by minimising the impact of random fluctuations and outliers on the final result.

When you take a measurement, there is always a degree of uncertainty involved. This uncertainty can be due to a variety of factors, such as the precision of the measuring instrument, the observer's ability to read the instrument, or random fluctuations in the quantity being measured. By taking multiple measurements and averaging them, you can reduce the impact of these uncertainties on your final result.

Imagine you're trying to measure the length of a piece of string. If you measure it once and get a result of 10cm, but then measure it again and get a result of 12cm, which one is correct? The truth is, neither of them might be exactly correct, but by averaging the two measurements (10cm + 12cm divided by 2), you get a result of 11cm, which is likely to be closer to the true length of the string than either of the individual measurements.

This is because when you average multiple measurements, the random errors (those that are equally likely to be too high or too low) tend to cancel each other out. For example, if one measurement is slightly too high and another is slightly too low, their average will be closer to the true value. This is known as the law of large numbers.

However, it's important to note that averaging measurements can only reduce random errors, not systematic errors (those that consistently skew the results in one direction). If your measuring instrument is consistently reading too high or too low, taking more measurements won't help. You'll need to calibrate your instrument or use a different method to reduce systematic errors.

In conclusion, averaging multiple measurements is a simple and effective way to reduce the impact of random errors and increase the accuracy of your results.