d2(N) is the expected value of the range of N observations from a normal population with standard deviation = 1. Thus, if r is the range of a sample of N observations from a normal distribution with standard deviation = σ, then E(r) = d2(N)σ.
d3(N) is the standard deviation of the range of N observations from a normal population with σ = 1. Thus, if r is the range of a sample of N observations from a normal distribution with standard deviation = σ, then stdev(r) = d3(N)σ.
Use the following table to find an unbiasing constant for a given value, N. (To determine the value of N, consult the formula for the statistic of interest.)
For values of N from 51 to 100, use the following approximation for d2(N):
For values of N from 26 to 100, use the following approximations for d3(N) and d4(N):
For more information on these constants, see the following:
D. J. Wheeler and D. S. Chambers. (1992). Understanding Statistical Process Control, Second Edition, SPC Press, Inc.
H. Leon Harter (1960). "Tables of Range and Studentized Range". The Annals of Mathematical Statistics, Vol. 31, No. 4, Institute of Mathematical Statistics, 1122−1147.
