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 |
Note: Details of the variance calculation:
338 = [52 + 72 + 82 + 102 + 102]
40 = [5 + 7 + 8 + 10 + 10]
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));