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wakiza33
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industrial Engineer // Berkeley Alumnus

Posts: 54
 Re: Who has more sisters?   « Reply #25 on: Sep 25th, 2014, 12:49pm » Quote Modify

With the slightly more girls than boys in the world, and an average of 2.4 kids--

Boys have more sisters, because of the '.4'. Because a girl can't be her own sister, boys will have more sisters.
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rmsgrey
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 Re: Who has more sisters?   « Reply #26 on: Sep 26th, 2014, 4:37am » Quote Modify

on Sep 25th, 2014, 12:49pm, wakiza33 wrote:
 With the slightly more girls than boys in the world, and an average of 2.4 kids--   Boys have more sisters, because of the '.4'. Because a girl can't be her own sister, boys will have more sisters.

That's only true in families with at least one of each - in a family with no girls, nobody has any sisters; in a family with no boys, the girls have at least as many sisters each as the boys.

Even within mixed families, the families with more sisters per child have more girls, so, for example, if you take two 7-child families: one with 5 girls; one with 5 boys, then the 7 girls have 22 sisters between them, while the 7 boys have 20, meaning that, despite it being true that each boy has more sisters than his sisters do, it's still true that, in those two families, girls have more sisters than boys.

The effect whereby a group can win in every category but lose on aggregate is known as Simpson's Paradox if you want to look into it more.

In the case of numbers of sisters, families with roughly even numbers of each are more common than families with more extreme splits, and, on aggregate, do give boys more sisters than girls, but that's balanced by the more extreme splits giving girls more sisters than boys, and, so long as there's no correlation between an individual's gender and the number and genders of their siblings, it all cancels out (in theory - I haven't actually run the numbers for a general case) and you end up with equal numbers.

In practice, you have places like China, where social policy has introduced a bias, and you have various biological mechanisms that also mess with the assumption that knowing a person's gender tells you nothing further about their siblings' genders, and there's always plain old random noise which will tend to prevent perfect equality, so the answer in the real world will probably be that one gender does have more sisters than the other, but it may not always be the same gender...
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wakiza33
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industrial Engineer // Berkeley Alumnus

Posts: 54
 Re: Who has more sisters?   « Reply #27 on: Sep 26th, 2014, 12:16pm » Quote Modify

Thanks for the info.

I knew my logic was incomplete, but couldn't progress further--I was waiting for someone to incur a deeper direction.
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