.. _statistics:
Statistics background
=======================
for understanding bandwidth scanners/generators
Standard deviation
-------------------
The formula for the sample standard deviation is
.. math::
s={\sqrt {\frac {\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}}{N-1}}}
where :math:`{x_{1},x_{2},\ldots ,x_{N}}` are the observed values of the
sample items, :math:`{\overline {x}}` is the mean value of these observations,
and N is the number of observations in the sample.
.. image:: 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
.. math::
z={x-\mu \over \sigma }
where:
μ is the mean of the population.
σ is the standard deviation of the population.
.. image:: images/The_Normal_Distribution.svg
[stdscore]_