HELP: Standard Deviation and Uncertainty of Measurements

[sAmurAi-X]

Physicists often utilise standard deviation to describe uncertainty of measurements. What advantages and disadvantages does this have?


I have bumped into a bottleneck while working on my physic lab report. I have been trying to google it out yet nothing much constructive could be retrieved. So, really appreciate if any of you could shed some light off my doubt. Much thanks in advance.

[bluez_aspic]

[[edited]]

[youngyew]

There is no "advantage" of standard deviation per se.

I guess the expected answer is along the line of "if we know the standard deviation, we would know how uncertain we are of the data, and make corresponding adjustment on the confidence we have on the ranges of answer we derive".

But then this is the advantage of "understanding and measuring uncertainty", not the advantage of uncertainty.

[sAmurAi-X]

Thanks, youngyew and bluez_aspic.

Actually, the question aforementioned requires the advantages of using standard deviation to describe uncertainty of measurements, instead of the advantage of uncertainty itself. In short, how could we use standard deviation to describe the uncertainty of our measurements and what're the advantages and disadvantages of doing this?

Thanks again:D

[bluez_aspic]

Thanks, youngyew and bluez_aspic.

Actually, the question aforementioned requires the advantages of using standard deviation to describe uncertainty of measurements, instead of the advantage of uncertainty itself. In short, how could we use standard deviation to describe the uncertainty of our measurements and what're the advantages and disadvantages of doing this?

Thanks again:D
The standard deviation is the most common, and perhaps natural, measure of statistical dispersion. i.e. it gives an indication as to how spread out the values of the measurements are. There's this famous inequality known as Chebyshev's inequality - in short, it states that it is unlikely that you'd have values deviating from the mean (average value) by many standard deviations.

The standard deviation can be sensitive to outlying observations though (coz you're taking the squared distance from the mean). Other forms of measure of dispersion - like the interquartile range, and the absolute deviation resolves this problem, however the standard deviation is easier to manipulate (algebraically and analytically, in the mathematical sense). This, among some other very compelling reasons.