It's defined as the root mean square of weighted deviations from the arithmetic mean.
Where X is the observed value and μ is the mean value. The standard deviation has the same unit of measurement of the observed values.It's a measure of the dispersion of the variable around its mean value, and expresses what is the error that you make on average taking the average value in place of the observed values.
Leti G., Statistica descrittiva, Il Mulino, 1999.
Guseo R., Statistica, CEDAM, 2006.
Editor: Giuliano DI TOMMASO