Order Statistics


        Goto:   Calculate     Output Format        Notes

Calculate Standard Deviation and Variance:              top





R (sample range)  
N (sample size)  


E[W] (expected value of W)

σ2 (variance)

  σ (standard deviation)  

Output Format:                                                        top

Select Format: Scientific Engineering Fixed

Notes:                                                                       top

bulletThis is an interesting application of statistics where you can estimate the variance of you sample based solely on the extremes of the sample.  If you want to estimate the standard deviation the traditional way look here.
bulletR is the sample range or the maximum value of your sample minus the minimum value.
bulletW=R/σ is the "standardized range".  E[W] is the expected value or mean of W and is a function only of the # of samples.
bulletThis analysis assumes the random variable is normal (i.e, has a gaussian distribution).
bulletSource of E[W] values is this table, which was provided to me by Dave L. Johnson of Titan, PSD.
bulletFrom the table cited above, you can also calculate the standard deviation of W, which tells you how good an estimate of σ you are making.  You can also figure out the probability that R is less than some number.


Copyright 2004-2005  Raymond J. Allen