The formula for calculating variance is:

The method of calculation may be more easily understood from the table below where the mean is 8.
i xi xi-mean (xi-mean)2
(index) (datum) (deviation) (squared deviation)
1 5 -3 9
2 7 -1 1
3 8 0 0
4 10 2 4
5 10 2 4
n=5 sum=40 0 18 

     
  • mean = 40/5 = 8
    • 
 
  • variance = (5*338 - 402)/(25-5) = 4.5
    • 
 
  • standard deviation = = 2.12
    •

Note: Details of the variance calculation:

338 = [52 + 72 + 82 + 102 + 102]
40 = [5 + 7 + 8 + 10 + 10]

Algorithm

Therefore a simple algorithm to calculate variance can be: 

double sum;
double sum_sqr;
double variance;
long n = data.length; // the number of elements in the data array (the actual syntax is language-specific)

for i = 0 to n
sum += data[i];
sum_sqr += ( data[i] * data[i] );
end for

variance = ((n * sum_sqr) - (sum * sum))/(n*(n-1));