Uncertainty in Measurement.
The uncertainty of a measurement expresses the range in which the true value of the quantity may lie.
Imagine we measure the time it takes for a ball to fall different heights through a liquid and get these readings for a particular height.
| Reading | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Time (s) | 3.30 | 3.34 | 3.10 | 3.23 | 3.45 | 3.34 | 3.25 | 3.44 | 3.23 | 3.19 |
We can calculate the degree of uncertainty statistically by considering the spread of results.
The mean of these readings is 3.39s. The lowest is 3.10 and the highest is 3.45. The median is around 3.25 which suggests that the errors are skewed towards the upper end.
This suggests an uncertainty of + or - 0.35s based on the maximum deviation from the mean. This is a 10.3% difference.
The standard deviation is 0.11s
We can also estimate the degree of uncertainty by considering the accuracy of our measuring instruments and the methods we use. The biggest error in this experiment, for example, was that human reaction time affected the readings. This is known to be about 0.3s for most people. A generous estimate would be 0.5s.
When we plot our graph of time against height we can express the degree of uncertainty using error bars as shown below.
The curve we draw, if we have identified all of the errors and what effect they might have, MUST go through all the bars.