Tell me about statistics

Shrews · September 2023

You maths types out there. Explain in laymans terms, not like you were sat the snug of the Rose and Crown with your boffin mates.

This is about gender.

So, the amount of men and women born are roughly 50/50, it never seems to be that we've gone 90/10 or, gulp, 99/1.

Now I would guess that 'statistically' some such anomaly will arise, let's say in the next million years, that one gender will hit at least a 90/10 population ratio one way or another.

But would I be guessing right, seeing as this doesn't seem to have happened before?

drofluf · September 2023

This is more of a biology question. A sperm has either an X (female) chromosome or a Y (male) chromosome and this determines the sex of the baby since all ova have only an X chromosome. So males have an XY chromosome pair, females XX.

In sperm on average the chromosomes are in a ratio of 105:100 Y:X so there are slightly more male births. But to move to a 90:10 ratio something would have to happen to eliminate the X or Y chromosomes from the male breeding population to favour one sex over the other.

Sassafras · September 2023

Depends on what sex they identify as.

ArchtopDave · September 2023

The "99" would have to form a very long queue, as I suspect the "1" would have a permanent headache.

SteveRobinson · September 2023

The greater the population the more likely it is to be 50:50 or thereabouts (given the above chromasome ratio and males' propensity to die earlier)

swiller · September 2023

Shrews said:

You maths types out there. Explain in laymans terms, not like you were sat the snug of the Rose and Crown with your boffin mates.

This is about gender.

So, the amount of men and women born are roughly 50/50, it never seems to be that we've gone 90/10 or, gulp, 99/1.

Now I would guess that 'statistically' some such anomaly will arise, let's say in the next million years, that one gender will hit at least a 90/10 population ratio one way or another.

But would I be guessing right, seeing as this doesn't seem to have happened before?

statistically, the more birth events, the less likely it will happen. Its the same as flicking a coin, the more you do it and the bigger the sample, the more likely it is to be 50/50 because that is the original possibility

thermionic · September 2023

@drofluf is right that the answer lies in biology, not statistics. The entry on “human sex ratio” on wikipedia makes for interesting reading. The ratio always tends toward an equilibrium of 1:1, which is explained by something called Fisher’s Principle. Interesting stuff.

swiller · September 2023

thermionic said:

@drofluf is right that the answer lies in biology, not statistics. The entry on “human sex ratio” on wikipedia makes for interesting reading. The ratio always tends toward an equilibrium of 1:1, which is explained by something called Fisher’s Principle. Interesting stuff.

It lies in both. You measure biological outcomes with statistics and learn more about biology in that process.
Familys hit the ops 90/10 all the time with 3+ kids all male or all female.
Drofluf is right that to change that on a global scale, would need an interference/new input into the process. But you know about that early by using statistics.

Tannin · September 2023

As @drofluf says, biology has a say in this, but leaving that aside and just looking at the maths, @swiller is spot on. The larger the numbers, the less likely an odd result is.

Think about it this way.

Start with a count of 1. With 1 child, the chance of getting either all-male or all-female is 100%.

Now consider a family of 2. You could have a girl first and then another girl, a girl and a boy, a boy and a girl, or a boy and another boy. The chance of an all-male family is 25% and the chance of an all-female family is 25%, so the total chance of having a one-sex family is 50%.

With a family of 4 you can have GGGG, GGGB, GGBG, GBGG, BGGG, GGBB, GBGB, and so on - 16 outcomes in total, only 2 of them (GGGG and BBBB) single sex. So the chance is 12.5%

With a family of 8, there are 256 possible outcomes (GGGGGGGG, GGGGGGGB, and so on) and only two of them single sex. So the chance is 0.78%.

(Hang on a minute. We have all heard of large families with every child a girl (or boy). Sure, but (a) 0.78% isn't that unlikely (if you had that chance of getting a flat tire on the way to work on any given day, you'd have to get out and put the spare on roughly twice a year), and we can't rule out biological causes - a man's balls can consistently produce mostly or even all X (female) sperm or Y sperm for medical reasons. But we are ignoring biology here so let's go back to the maths.)

Now think about 16 children. Now we have 65,536 possible outcomes, but still only 2 are single sex. So the chance of all of them being male or female is 0.00076%

With 20 children it is 0.000048. With 30 children it's 0.000000047%. With the population of a small city, you'd start with a decimal point and then write zeros until your pen ran out of ink. With the population of the UK, you'd have a decimal point followed by so many zeros that the world couldn't make enough paper to print them on.

Shrews · September 2023

swiller said:

Shrews said:

You maths types out there. Explain in laymans terms, not like you were sat the snug of the Rose and Crown with your boffin mates.

This is about gender.

So, the amount of men and women born are roughly 50/50, it never seems to be that we've gone 90/10 or, gulp, 99/1.

Now I would guess that 'statistically' some such anomaly will arise, let's say in the next million years, that one gender will hit at least a 90/10 population ratio one way or another.

But would I be guessing right, seeing as this doesn't seem to have happened before?

statistically, the more birth events, the less likely it will happen. Its the same as flicking a coin, the more you do it and the bigger the sample, the more likely it is to be 50/50 because that is the original possibility

So, just using that coin toss example

If I tossed a coin a million times, one per year, then what is the likelihood that at some point there will be a run of 80 tosses that land on heads?

(And if heads were men then 80 years of just men being born effectively wiping out the human race as no women around to give birth)

notanon · September 2023

An interesting question in the context of climate change (thanks to biden for making official recently)

"In crocodilians the temperature of egg incubation is the environmental factor determining sex. If the temperature is cool, around 30 °C, the hatchlings are all female. Warmer temperatures, around 34 °C, hatch all males."

Tannin · September 2023

^ Many other creatures have a similar system. Quite a few birds, for example.

Humans, however, have a different system which is purely genetic. The mother provides a single chromosome which we call "X". The father also provides a single chromosome which can be either another X or a different one we call "Y". Any given sperm cell contains one or the other, not both. Pairing of X with X results in a female baby, X and Y produces a male. (There are also 44 other human chromosomes, but these have nothing to do with sex determination.)

Nearly all placental mammals use the same XY system (eutherians such as humans, cows, cats, and mice, and marsupials such as quolls, wallabies, and opossums). A handful of small, obscure placentals use a system where XX = female and a single X (with no matching chromosome) makes a male.

The monotremes (egg laying mammals) have a very complicated system involving 10 sex chromosomes which nobody properly understands yet.

Some insects and some fish use a system similar to the mammalian one. For others, sex is determined by environmental factors.

Tannin · September 2023

Shrews said:

So, just using that coin toss example

If I tossed a coin a million times, one per year, then what is the likelihood that at some point there will be a run of 80 tosses that land on heads?

(And if heads were men then 80 years of just men being born effectively wiping out the human race as no women around to give birth)

The chance of getting 80 heads in a row if you try just once is 0.000000000000000082718%

But you are trying it a million times (well, actually 999,920 times, close enough to a million for our purposes) so your odds of getting 80 heads running goes up to 0.000000000082716%. However we are interested in getting lots of males OR females in a row, so we need to count both heads and tails, which gives us a 0.00000000000000165433% chance of success.

I got dizzy counting those zeros and don't promise that's exactly right. You can check by calculating 100/(2^80)*2 and then multiply that by (number of years - 80).

guitargeek62 · September 2023

Sassafras said:

Depends on what sex they identify as.

Sex is genetic (and yes, there’s still more than two), but gender is a social construct and can be whatever the hell you want it to be.

Note: @Shrews, this is about sex, not gender. They are not the same.

Tannin · September 2023

^ Correct weight.

horse · September 2023

Shrews said:

swiller said:

Shrews said:

You maths types out there. Explain in laymans terms, not like you were sat the snug of the Rose and Crown with your boffin mates.

This is about gender.

So, the amount of men and women born are roughly 50/50, it never seems to be that we've gone 90/10 or, gulp, 99/1.

Now I would guess that 'statistically' some such anomaly will arise, let's say in the next million years, that one gender will hit at least a 90/10 population ratio one way or another.

But would I be guessing right, seeing as this doesn't seem to have happened before?

statistically, the more birth events, the less likely it will happen. Its the same as flicking a coin, the more you do it and the bigger the sample, the more likely it is to be 50/50 because that is the original possibility

So, just using that coin toss example

If I tossed a coin a million times, one per year, then what is the likelihood that at some point there will be a run of 80 tosses that land on heads?

(And if heads were men then 80 years of just men being born effectively wiping out the human race as no women around to give birth)

There's more than 1 baby born each year though - so the odds become pretty much impossible

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