Chimactiv - Interactive numerical educational resources for the analysis of complex media

Statistics reminders

For a series of n measurements of the same measurand (x_i is the result of i^th measurement i): the mean value of these measurement results is chosen as the best estimate of the measurand value

Mean

$\LARGE \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x{_{i}}$

Standard deviation associated with this mean value

$\LARGE s = \sqrt{ \frac{1}{n - 1} \sum_{i=1}^{n} ( x{_{i}} - \bar{x}){^{2}} }$

The standard deviation is expressed in the same unit of measurement as the data.

Variance

$\LARGE s{^{2}}(x) = \frac{1}{n - 1} \sum_{i=1}^{n} ( x{_{i}} - \bar{x}){^{2}}$