Dtandard Error
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Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book Wolfram Web Resources» 13,594 entries Last updated: Tue standard error formula Sep 27 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Probability standard error calculator and Statistics>Moments> Interactive Entries>Interactive Demonstrations> Standard Error There appear to be two different definitions of the
Standard Deviation
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
Standard Error Vs Standard Deviation
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 standard error excel the quantity, (Kenney and Keeping 1951, p.187; Zwillinger 1995, p.626). SEE ALSO: Estimator, Population Mean, Probable Error, Sample Mean, Standard Deviation, Variance 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. http://mathworld.wolfram.com/StandardError.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical. Wolfram|Alpha» Explore anything with the first computational knowledge engine. Wolfram Demonstrations Project» Explore thousands of free applications across science, mathematics, e
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from the same population. The standard error of http://support.minitab.com/en-us/minitab/17/topic-library/basic-statistics-and-graphs/hypothesis-tests/tests-of-means/what-is-the-standard-error-of-the-mean/ the mean estimates the variability between samples whereas the standard deviation measures the variability within a single sample. For example, you have http://davidmlane.com/hyperstat/A103735.html a mean delivery time of 3.80 days with a standard deviation of 1.43 days based on a random sample of 312 delivery standard error times. These numbers yield a standard error of the mean of 0.08 days (1.43 divided by the square root of 312). Had you taken multiple random samples of the same size and from the same population the standard deviation of those different sample means would standard error formula be around 0.08 days. Use the standard error of the mean to determine how precisely the mean of the sample estimates the population mean. Lower values of the standard error of the mean indicate more precise estimates of the population mean. Usually, a larger standard deviation will result in a larger standard error of the mean and a less precise estimate. A larger sample size will result in a smaller standard error of the mean and a more precise estimate. Minitab uses the standard error of the mean to calculate the confidence interval, which is a range of values likely to include the population mean.Minitab.comLicense PortalStoreBlogContact UsCopyright © 2016 Minitab Inc. All rights Reserved.EnglishfrançaisDeutschportuguêsespañol日本語한국어中文(简体)By using this site you agree to the use of cookies for analytics and personalized content.Read our policyOK
the standard deviation of the original distribution and N is the sample size (the number of scores each mean is based upon). This formula does not assume a normal distribution. However, many of the uses of the formula do assume a normal distribution. The formula shows that the larger the sample size, the smaller the standard error of the mean. More specifically, the size of the standard error of the mean is inversely proportional to the square root of the sample size.