\sigma_{n-1} \ = \ 
\vcenter {
  \sqrt {
    \displaystyle
    \sum \limits _ {i=1} ^N
    {
      \left (
        x - 
        \overline x 
      \right )
    }
    ^ 2
  \over
    \displaystyle 
     N-1
  }
}
\ = \ 
\vcenter {
  \sqrt {
    \displaystyle
    N \sum \limits _ {i=1} ^N 
    \left( x_i \right)^2 - 
    \left(
    \sum \limits _ {i=1} ^N x_i 
    \right)
    ^2
  \over
    \displaystyle 
    N \left (N-1 \right)
  }
}