How to work on the Nth column of a file with awk?

Consider the following awk script called stat.awk:
#
# AWK SCRIPT stat_general.awk does statistics... 
# prints out arithmetic mean, standard deviation,
# standard error of column 1
#

BEGIN { n = 0; s = 0; ss = 0;}
{ 
  n++;
  s += $1;
  ss += $1 *$1;
}
END {
   print n " data points"
   m = (s+0.0)/n; print m " average"
   sd = sqrt( (ss - n * m * m) / ( n - 1.0))
   print sd " standard deviation"
   se = sd/sqrt(n)
   print se " standard error"
}


$ awk -f stat.awk

This prints out the statistics of column 1.

What if we wanted to find the statistics of an arbitrary column ColumnNum (especially if you want to wrap it in a bash script for repeated operation)? It is reasonably straightforward to modify the script above to stat_general.awk

#
# AWK SCRIPT stat_general.awk does statistics... 

# prints out arithmetic mean, standard deviation,
# standard error of an arbitrary column

#

BEGIN { n = 0; s = 0; ss = 0;}
{ 

  n++;

  s += $ColumnNum;

  ss += $ColumnNum *$ColumnNum;

}

END {
   print n " data points"
   m = (s+0.0)/n; print m " average"
   sd = sqrt( (ss - n * m * m) / ( n - 1.0))
   print sd " standard deviation"
   se = sd/sqrt(n)
   print se " standard error"
}

$ x=5
$ awk -f stat_general.awk -v ColumnNum=$x

Presto!