Formula for standard deviation sample calculation is:
SD = sqrt (( ∑( x - m)²) / ( n - 1 )),
where x stays for each value in the data set, m stays for mean of all values in the data set, and n stays for the number of values in the data set.
For example: Find the sample standard deviation for the set of numbers: 10, 11, 11, 12, 12.
First we will find mean of all avlues: m = ( 10 + 11 + 11 + 12 +12 ) / 5 = 11.2
SD = sqrt (( 1.2² + 0.2² + 0.2² + 0.8² + 0.8² ) / ( 5 - 1 ))=
= sqrt ( 2.8 / 4 ) = √0.7 = 0.837
