B How to calculate a random measurement error?

AI Thread Summary
The discussion centers on two formulas for measuring random error: the standard deviation and the mean absolute deviation. The standard deviation formula, which is the first one presented, is the conventional method for calculating variability in data sets. The mean absolute deviation, while simpler and sometimes used in machine learning for efficiency, is less common in fields like experimental physics. Participants agree that for accurate scientific measurements, the standard deviation is the preferred choice. Overall, the standard deviation is emphasized as the more reliable metric for error calculation.
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How to calculate a random measurement error? If we did a measurement and want to calculate a random error, what formula are we to use?
I have seen this formula

$$\sigma=\sqrt{\frac {\sum_{i=1}^{N}{(X_i- \bar{X})^2}}{N(N-1)}}$$

but also this formula $$\sigma =\frac{\sum_{i=1}^{N}{|X_i- \bar {X}|}}{N}.$$ Which of them is correct?
 
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The first one :smile:

##\ ##
 
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The first one is the standard deviation. That is the usual one. The second one is the mean absolute deviation and it is rarely used at all.
 
Dale said:
The second one is the mean absolute deviation and it is rarely used at all.
Some machine learning applications seem to use it - I think because it's cheaper to calculate, so it gives you a time saving if you can live with the less mathematically nice behaviour. But in experimental physics I agree it's a no, you want the standard deviation.
 
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