There appear to be two different definitions of the standard error.
The standard error of a sample of sample size 
is the sample's standard
deviation divided by 
.
It therefore estimates the standard deviation
of the sample mean based on the population
mean (Press et al. 1992, p. 465). Note that while this definition
makes no reference to a normal distribution,
many uses of this quantity implicitly assume such a distribution.
The standard error of an estimate may also be defined as the square root of the estimated error variance 
of the quantity,
(Kenney and Keeping 1951, p. 187; Zwillinger 1995, p. 626).
See also
Estimator,
Population Mean,
Probable Error,
Sample
Mean,
Standard Deviation,
Variance
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References
Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, 1962.Kenney,
J. F. and Keeping, E. S. "Standard Error of the Mean." §6.5
in Mathematics
of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 110
and 132-133, 1951.Press, W. H.; Flannery, B. P.; Teukolsky,
S. A.; and Vetterling, W. T. Numerical
Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England:
Cambridge University Press, 1992.Zwillinger, D. (Ed.). CRC
Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, 1995.Referenced
on Wolfram|Alpha
Standard Error
Cite this as:
Weisstein, Eric W. "Standard Error." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StandardError.html
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