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r = σ/|x|, where x is not equal to 0. In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean value of ...
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Relation of an error bar to PDF shape. The error bar on a plot is most often meant to represent the ±1 uncertainty on a data point. Bayesians and frequentists will disagree on what that means. If data is distributed normally around “true value”, it's clear what is intended: exp[-(x- )2/2 2].
Basically, there's an interval surrounding your measurement where the true value is expected to lie. If your measurements give experimental uncertainties of 0.1 and 1.0 respectively, the new measured values may be expressed 2:5 0:1 and 1:5 1:0.
p x = –x p 2x; which leads to p x = 10 § 0:4. The fallacy here is that the two factors p x have the same errors, and the addition in quadrature rule requires that the various errors be independent. 10/5/01 6
For a digital device which directly outputs a reading (like a digital scale), you can take the uncertainty to be given by the last digit the device outputs. For instance, if it reads 4:18, then the uncertainty would be 0:01 (in whatever units the scale reads).
In words, the error in the estimated mean is equal to the error in each individual measurement X divided by the square root of the number of times the measurement was repeated. Sometimes is called the standard error of the mean .
