What is the mean and standard deviation for men's and then women's standard FIDE ratings for those 2000 and above?

Question

From this answer, the unconditional means and standard deviations are

Female
Mean = 1505, standard deviation = 339

Male
Mean = 1675, standard deviation = 346

What about the case for ratings of 2000+ ?

Let's do...

1. preferably for as of...Apr2021, same month as the above computations, if it's hard to repeat the above for as of Sep2021 and then

2. as of Sep2021 if it's not so hard to repeat above Apr2021 computations for Sep2021?

(Basically E[X|X=>2000] and square root of Var[X|X=>2000])

And actually while we're at it may we please also see these?

1. 1900 up?

2. 1800 up?

3. 1700 up?

4. 1600 up?

5. 1500 up?

Answer 1

Using the April 2021 FIDE data:

Rating Range Female Mean/Standard Deviation Male Mean/Standard Deviation
1500+ F 1817/213, M 1870/230
1600+ F 1879/188, M 1919/207
1700+ F 1940/163, M 1972/184
1800+ F 2004/137, M 2030/162
1900+ F 2062/114, M 2091/141
2000+ F 2116/100, M 2156/122

Note that for females 1500+ basically corresponds to the top half of the normal curve whereas for males it includes a significant chunk (about half a standard deviation) of the lower half