standard deviation in awk

BEGIN {
    sum = 0;
    n = 0;
    sqOfSums = 0;
}
{
    sum += $1;
    nums[n] = $1
    n += 1;
}
END {
    mean = sum / n;
    for (i = 0; i < n; i++) {
        localVarience = nums[i] - mean;
        sqOfSums += ( localVarience * localVarience );
    }
    variance = sqOfSums / ( n - 1 );
    standardDeviation = sqrt(variance);
    minimumSd = mean - standardDeviation;
    maximumSd = mean + standardDeviation;
    populationSd = sqrt(sqOfSums / n);
    print "Standard Deviation:"standardDeviation;
    print "Minimum SD:        "minimumSd;
    print "Maximum SD:        "maximumSd;
    print "Population SD:     "populationSd;
}