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Empirical Rule


lyric © 2017 Lawrence M. Lesser
may sing to the tune of “Material Girl” (Peter Brown and Robert Rans, popularized by Madonna)

Data values  normally are 
no more far away
Than 3 standard  deviations  
from the mean displayed.
And within 2 deviations, 19 of 20 lie, that’s right!
And within 1  deviation,  2/3 are confined,  

CHORUS:
‘Cause we are living in an empirical world
and I need an empirical tool.
You know that we are living in an empirical world
and I use the empirical rule!

If I think a  population
looks bell curve to me,
The rule helps tag outliers like a
z-score more than 3.
But if the population may not
take the normal shape (no way!),
Frequencies that  you expect can
help you ascertain 

(Repeat Chorus)