I do not know where to put this thread in a computer chess forum, so if moderation is needed, it will be welcomed. I calculated the average and the standard deviation of FIDE rating list ratings (downloads here) with a small programme in Fortran 95. Here is the code:

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```
program normal
implicit none
integer::i
integer,parameter::n=141286
real(KIND=3)::Elo(1:150000),sum, average, s, sum2, t0, t1, time
t0=cpu_clock@()
open(unit=111,file='outT.txt',status='unknown',action='read')
do i=1,n
read(111,*) Elo(i)
end do
sum=0d0
do i=1,n
sum=sum+Elo(i)
end do
average=sum/(n+0d0)
sum2=0d0
do i=1,n
sum2=sum2+(Elo(i)-average)*(Elo(i)-average)
end do
s = sqrt(sum2/(n-1d0))
t1=cpu_clock@()
time=(t1-t0)/3d9 ! 3 GHz.
open(unit=110,file='Results.txt',status='unknown',action='write')
write(110,'(A,I6,A)') 'Number of rated players: ', n,'.'
write(110,*)
write(110,'(A)') 'µ: average; s: standard deviation.'
write(110,*)
write(110,'(A,F7.2,A,F6.2)') 'µ ~ ', 1d-2*nint(1d2*average,KIND=3), '; s ~ ', 1d-2*nint(1d2*s,KIND=3)
write(110,*)
write(110,'(A,I3,A)',advance='no') 'Finished. Approximated elapsed time: ', nint(1d3*time,KIND=3), ' ms.'
close(110)
end program
```

**txtTruncate**by Norm Pollock was fundamental, so thank you very much. This programme did its calculations between 0.1 and 0.14 seconds more less (each time), so I consumed more time in downloading the lists and preparing (truncating) them than in the calculations; the consumed time in writing this source code was low because it is somewhat trivial. Inactive players are included because I did not know how to filter them...

I have always found interesting this ChessBase article although I have not read it carefully. I know that rating inflation exists, but comparing averages of rating lists between January 2009 and May 2012, these averages are decreasing! I suppose that it is due to the increasing number of players (most of them novice) that should decrease the average rating; standard deviations also grow, maybe due to those novice players with lower rating. I have obtained the following results (rounded up to 0.01 Elo):

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```
January 2009:
Number of rated players: 99232.
µ: average; s: standard deviation.
µ ~ 2044.50; s ~ 197.59
Finished. Approximated elapsed time: 99 ms.
```

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```
April 2009:
Number of rated players: 99997.
µ: average; s: standard deviation.
µ ~ 2038.43; s ~ 200.33
Finished. Approximated elapsed time: 98 ms.
```

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```
July 2009:
Number of rated players: 105242.
µ: average; s: standard deviation.
µ ~ 2031.04; s ~ 204.44
Finished. Approximated elapsed time: 104 ms.
```

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```
September 2009:
Number of rated players: 107392.
µ: average; s: standard deviation.
µ ~ 2023.92; s ~ 207.77
Finished. Approximated elapsed time: 111 ms.
```

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```
November 2009:
Number of rated players: 99522.
µ: average; s: standard deviation.
µ ~ 2016.46; s ~ 209.09
Finished. Approximated elapsed time: 97 ms.
```

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```
January 2010:
Number of rated players: 109556.
µ: average; s: standard deviation.
µ ~ 2014.49; s ~ 211.47
Finished. Approximated elapsed time: 107 ms.
```

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```
March 2010:
Number of rated players: 113629.
µ: average; s: standard deviation.
µ ~ 2011.87; s ~ 213.11
Finished. Approximated elapsed time: 112 ms.
```

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```
May 2010:
Number of rated players: 116524.
µ: average; s: standard deviation.
µ ~ 2007.00; s ~ 214.82
Finished. Approximated elapsed time: 114 ms.
```

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```
July 2010:
Number of rated players: 119042.
µ: average; s: standard deviation.
µ ~ 2001.75; s ~ 217.48
Finished. Approximated elapsed time: 117 ms.
```

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```
September 2010:
Number of rated players: 121878.
µ: average; s: standard deviation.
µ ~ 1995.43; s ~ 220.68
Finished. Approximated elapsed time: 120 ms.
```

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```
November 2010:
Number of rated players: 123519.
µ: average; s: standard deviation.
µ ~ 1991.60; s ~ 222.55
Finished. Approximated elapsed time: 121 ms.
```

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```
January 2011:
Number of rated players: 122615.
µ: average; s: standard deviation.
µ ~ 1986.24; s ~ 225.15
Finished. Approximated elapsed time: 119 ms.
```

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```
March 2011:
Number of rated players: 126695.
µ: average; s: standard deviation.
µ ~ 1982.77; s ~ 227.06
Finished. Approximated elapsed time: 125 ms.
```

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```
May 2011:
Number of rated players: 129843.
µ: average; s: standard deviation.
µ ~ 1977.59; s ~ 229.26
Finished. Approximated elapsed time: 127 ms.
```

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```
July 2011:
Number of rated players: 132263.
µ: average; s: standard deviation.
µ ~ 1972.49; s ~ 231.96
Finished. Approximated elapsed time: 131 ms.
```

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```
September 2011:
Number of rated players: 135353.
µ: average; s: standard deviation.
µ ~ 1966.51; s ~ 234.73
Finished. Approximated elapsed time: 136 ms.
```

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```
November 2011:
Number of rated players: 137694.
µ: average; s: standard deviation.
µ ~ 1961.87; s ~ 237.12
Finished. Approximated elapsed time: 139 ms.
```

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```
January 2012:
Number of rated players: 139007.
µ: average; s: standard deviation.
µ ~ 1956.57; s ~ 239.41
Finished. Approximated elapsed time: 137 ms.
```

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```
March 2012:
Number of rated players: 141286.
µ: average; s: standard deviation.
µ ~ 1952.70; s ~ 241.44
Finished. Approximated elapsed time: 139 ms.
```

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```
May 2012:
Number of rated players: 145026.
µ: average; s: standard deviation.
µ ~ 1947.04; s ~ 243.21
Finished. Approximated elapsed time: 138 ms.
```

Any insight, comment... will be welcomed.

Regards from Spain.

Ajedrecista.