I would like to know, for each country, for each of the sexes male and female or other sex, what are the percentage of males and of females or other sex, the percentage of infertile males and infertile females or other sex, the percentage of children less fertile and childless infertile people and so on. I also would like to see a mean age till fertility and till infertility for each sex, possibly with distributions of these data.

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The sex ratio represents the percentage of men and women by country. http://statisticstimes.com/population/countries-by-sex-ratio.php

General data for infertility is available. http://globalfertilitymap.com/

Currently, the data on global male infertility is lacking—both in terms of prevalence estimates and men’s experiences across cultures—simultaneously contributing to and reinforcing gender-related stigma https://www.mhtf.org/2017/01/18/the-burden-of-infertility-global-prevalence-and-womens-voices-from-around-the-world/

Fertility rates for women is available by country and age group. http://www.un.org/en/development/desa/population/theme/fertility/index.shtml

The UN data also includes information on childlessness. http://www.pewresearch.org/fact-tank/2014/01/03/in-terms-of-childlessness-u-s-ranks-near-the-top-worldwide/

This doesn’t answer all of your question, but I think it catches some of what you want.

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