#!/usr/bin/awk -f

### mean.awk
# calculate mean average

BEGIN {
    #OFMT = "%.18g"
    sign = "[+-±]?"
    decimal = "[0-9]+[.]?[0-9]*"
    fraction = "[.][0-9]*"
    exponent = "([Ee]" sign "[0-9]+)?"
    number = "^" sign "(" decimal "|" fraction ")" exponent "$"
}

# Welford's 'online' algorithm for variance
NF > 0 {
    for (m=1; m<=NF; m++) {
        if (m ~ number) {
            count += 1
            delta0 = $m - mean
            mean = mean + delta0/count
            delta1 = $m - mean
            M2 = M2 + delta0*delta1
            if (count > 1)
                var = M2/(count - 1)
            else
                var = "nan"
        }
    }
}

END {
    print "mean", "std_dev", "std_err", "count"
    print mean, sqrt(var), sqrt(var/count), count
}