RE: Tchebychev Inequality

[Steven_S_Prevette@rl.gov]

The Tchebychev Inequality states that no matter what the distribution is of
the data, no more than 1/n-squared of the data will be outside n standard
deviations from the average.  For n=3, no more than one ninth of the data
will be outside 3 standard deviations from the average.  

Acheson Duncan's Quality Control and Industrial Statistics has a
mathematical proof, starting with the statistical formula for standard
deviation.

The Camp-Meidel extension states that a continuous distribution,
monotonically decreasing from a single central peak (unimodal) will have no
more than 1/(2.25 x n-squared) of the data outside on n standard deviations
from the average.

Steve Prevette
QA Engineer, ESH Radiological Compliance
Fluor Hanford, A Fluor Global Services Company
ASQ Certified Quality Engineer
steven_s_prevette@rl.gov
509-373-9371