https://www.wmo.int/pages/prog/gcos/documents/gruanmanuals/UK_NPL/mgpg11.pdf
Uncertainty of measurement is the doubt that exists about the result of any measurement. You might think that well-made rulers, clocks and thermometers should be trustworthy, and give the right answers. But for every measurement - even the most careful - there is always a margin of doubt. In everyday speech, this might be expressed as ‘give or take’ ... e.g. a stick might be two metres long ‘give or take a centimetre’.
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Uncertainty is a quantification of the doubt about the measurement result.
Since there is always a margin of doubt about any measurement, we need to ask ‘How big is the margin?’ and ‘How bad is the doubt?’ Thus, two numbers are really needed in order to quantify. One is the width of the margin, or interval. The other is confidence level.
For example. We might say that the length of a certain stick measures 20 centimetres plus or minus 1 centimetre, at 95 percent confidence level. This result could be written:
20 cm ±1 cm, at a level of confidence of 95%.
The statement says that we are 95 percent sure that the stick is between 19 centimetres and 21 centimetres long.