stat: standard deviation

[Petr M. <mi...@ph...>]

In gnuplot, the "stat" command calculates "Std Dev:" and "STATS_stddev_x" as
     sqrt( SumOfSquares / n )

In GNU R, OpenOffice et al, the function stddev() calculates
     sqrt( SumOfSquares / (n-1) )
while function stddevp() returns
     sqrt( SumOfSquares / n )

That's confusing. Why has gnuplot chosen the other possibility (this smaller
stddev estimate means that the average value of the statistical ensemble
is known).

What to do with that?

- It would be nice if gnuplot gets compatible and has both
   "Std Dev:" and "STATS_stddev_x" and "Std Dev P:" and "STATS_stddevp_x".
   But then scripts running on different gnuplot versions would give
   different results :-(

- Let gnuplot write both variants of stddev so that the user sees which
   values is which type of stddev (one is smaller and the other is larger). The
   other could be called "Std Dev (n-1):" and "STATS_stddev1_x".

- Document stddev used in gnuplot by writing its formula in the help.

- I would also like if gnuplot writes the deviation of the mean
   as used in (mean +- err)  where err=sqrt(SumOfSquares/(n*(n-1))).
   How to call this value?

Well, I figured this out when preparing some hints for students...

---
Petr Mikulik