#!/bin/sh
# check that a series of random numbers is normal by computing and printing:
# the mean (should be 0.0)
# the variance (should be 1.0)
# the count within one standard deviation (should be 68.3%)
# the count within two standard deviations (should be 95.4%)

awk '
{sum += $1; sum2 += $1 * $1;}
$1 >= -1 && $1 <= 1 {w1 ++;}
$1 >= -2 && $1 <= 2 {w2 ++;}
END {print sum / NR, (sum2 * NR - sum * sum) / NR / NR, w1 / NR, w2 / NR;}
' "$@"