#!/usr/bin/awk -f

### mean.awk
# calculate mean average of serialized input

BEGIN {
    OFS = FS
    #sign = "[+-]?"
    #decimal = "[0-9]+[.]?[0-9]*"
    #fraction = "[.][0-9]*"
    #exponent = "([Ee]" "[+-]?" "[0-9]+)?"
    number = "^[+-]?([0-9]+[.]?[0-9]*|[.][0-9]*)([Ee][+-]?[0-9]+)?$"
}

# Welford's 'online' algorithm for variance
NF {
    for (n=1; n<=NF; n++) {
        if ($n ~ number) {
            count += 1
            (count == 1 || $n < min) ? min = $n : min = min
            (count == 1 || $n > max) ? max = $n : max = max
            range = max - min
            delta0 = $n - mean
            mean += delta0/count
            delta1 = $n - mean
            M2 += delta0*delta1
            (count > 1) ? var = M2/(count - 1) : var = "nan"
        }
    }
}

END {
    print "mean", "std_err", "std_dev", "range", "min", "max", "total", "count"
    print mean, sqrt(var/count), sqrt(var), range, min, max, (mean*count), count
}