Slide 27 of 250

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.

s = sigma = Standard Deviation

Finding the Standard Deviation

Mean

s = 0.070

Mean

s = 0.80

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