8/18/2019 Calculating Statistical Mean and Standard Deviation in
One Pass
1/2
Calculating statistical mean and standard deviation inone
pass
Mean formula : sigma(i, 1, n, xi)/n
Standard deviation formula : sqrt(sigma(i, 1, n,
(xi-mean)^2)/(n-1))
LetSum = sigma(i, 1, n)
ThenMean = sum / n
Decompose SD
Sqr(sd) = sigma(i, 1, n, (xi-sum/n)^2 / (n-1)
Sqr(sd) = sigma(i, 1, n, ((n*xi-sum)/n)^2 / (n-1)
Sqr(sd) = sigma(i, 1, n, (n*xi-sum)^2 / n^2) / (n-1)
Sqr(sd) = sigma(i, 1, n, (n*xi-sum)^2) / ((n^2) * (n-1))
Sqr(sd) = sigma(i, 1, n, (n*xi)^2-2*(n*x[i])*sum+sum^2)) /
((n^2) * (n-1))
Sqr(sd) = sigma(i, 1, n, (n*xi)^2)-2*n*sum * sigma(i, 1, n,
xi) + sigma(i, 1, n, sum^2)) / ((n^2) * (n-1))
Sqr(sd) = ((n^2)*sigma(i, 1, n, (xi)^2) - 2*n*sum^2 +
n*sum^2) / ((n^2) * (n-1))
Sqr(sd) = n*(n*sigma(i, 1, n, (xi)^2) - 2 *sum^2 + sum^2) /
((n^2) * (n-1))
Sqr(sd) = (n*sigma(i, 1, n, (xi)^2) - sum^2) / (n*(n-1))
Algorithmi traversal[1..n]
SUM = SUM + !iSUM2 = SUM2 + !i*!i
"#$%"&$ = SUM / n
#"%'"$ = (n * SUM2 SUM * SUM) / (n * ( n 1))
