Statistics background

for understanding bandwidth scanners/generators

Standard deviation

The formula for the sample standard deviation is

s={\sqrt {\frac {\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}}{N-1}}}

where {x_{1},x_{2},\ldots ,x_{N}} are the observed values of the sample items, {\overline {x}} is the mean value of these observations, and N is the number of observations in the sample.

_images/Comparison_standard_deviations.svg

[stdev]

Standard score

If the population mean and population standard deviation are known, the standard score of a raw score x[1] is calculated as

z={x-\mu \over \sigma }

where:

μ is the mean of the population. σ is the standard deviation of the population.

_images/The_Normal_Distribution.svg

[stdscore]