Standard Deviation

Standard deviation, abbreviated as \(\sigma\) (Greek symbol sigma), measures how spread out the data is.

 

Standard Deviation formulas

\(\large{ \sigma = \sqrt{  \frac{ \sum \; \left( X_s \;-\; m \right)^2  }{ n }     }  }\)
\(\large{ \sigma = \sqrt{  \frac{ 1 }{ n } \; \sum_{s=1}^n  \;  \left( X_s \;-\; m \right)^2      }   }\)

Where:

\(\large{ \sigma }\) = standard deviation

\(\large{ \sum \;X_s }\)  (Greek symbol Sigma) = sum of data values  \(\large{ X_1, X_2, X_3, ... }\)

\(\large{ m }\) = mean value

\(\large{ n }\) = number of data values