#!/usr/bin/awk -f 

# Data averaged is the first column of the numbers provided
# Gives average and error for uncorrelated data.
# Careful: Empty lines will give wrong result! How to go around that? 

{ 
  av += $1;    # the sum of data
  er += $1*$1;  # the sum of squares of data
}
END{

  #we assume NR is the number of data (wrong if empty lines)
  av /= NR;
  er /= NR;
  # formula for error of uncorrelated measurements
  er  = sqrt( (er - av*av)/(NR-1) ); 
  print av, "+/-", er;

}