Algorithms For Calculating Variance

$\backslash mathrm\{Variance\}\; =\; \backslash frac\; \{n\backslash sum\_\{i=1\}^\{n\}\; x\_i^2\; -\; (\backslash sum\_\{i=1\}^\{n\}\; x\_i)^2\}\{n^2\}.$

$\backslash mathrm\{Variance\}\; =\; \backslash frac\; \{n\backslash sum\_\{i=1\}^\{n\}\; x\_i^2\; -\; (\backslash sum\_\{i=1\}^\{n\}\; x\_i)^2\}\{n(n-1)\}.$

   
mean = 40/5 = 8
   
variance = (5 · 338 − 402)/(5 · 4) = 4.5
   
standard deviation = $\backslash sqrt\{\backslash mathrm\{Variance\}\}\; =\; 2.12$
 

Algorithm

  long n = 0;  double sum = 0;  double sum_sqr = 0;  double variance;    foreach x in data:    n += 1;    sum += x;    sum_sqr += x*x;  end for    variance = (sum_sqr - sum*sum/n)/(n-1); 

Algorithm

double avg = 0; double var = 0; long n = data.length; // number of elements  for i = 1 to n 
  avg = (avg*i + datai) / (i + 1);  var = (var * (i - 1) + (datai - avg)*(datai - avg)) / i; 
 end for  return var; // resulting variance 

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