© 2004 Cayman Business
Systems
Rev:
Pre-G3 - Rendered Thursday,
February 12, 2004
Slide 27
Elsmar.com --- The
Cove!
8-Disciplines Problem Solving
Elsmar.com
Standard Deviation
The most common
measure of dispersion. The standard deviation is the square root of the variance, which is the sum
of squared distances between each datum
and the mean, divided by the sample size minus one.
For a tiny sample of three values (1,2,15), the mean is:
(1 + 2
+ 15)/3 = 6
and the variance is
((1 -
6)^2 + (2 - 6)^2 + (15 - 6)^2) / (3 - 1) = 61
The standard
deviation (s) is not a very helpful measure of spread for distributions in general. Its
usefulness is due to its
intimate connection with a special type of distribution, namely to the normal distribution.
The standard
deviation is more sensitive to a few extreme
observations than is the mean. A skewed distribution with a few values in the 'long tail' will have large standard deviation and it will not provide much helpful information in such cases.
X = X-Bar = Mean
s = sigma = Standard Deviation
Finding
the Standard Deviation
Mean
s = 0.070
Mean
s = 0.80