Measuring uncertainty

Ada Chen · Research notes

A measurement is useful when we know how much confidence to place in it.

Repeated observations

Take several readings under the same conditions. Their spread tells us something that a single value cannot.

Trial Reading
A 4.2
B 4.4
C 4.1

The sample spread gives us a useful summary:

s=1n−1∑i=1n(xi−xˉ)2.s = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2}.

Report what remains

Keep the original readings beside the summary. Precision describes the instrument; uncertainty describes what we still do not know.