Maths Problem

[Lul Thyme]

Yes Krazyhorse.
But thats only part of the thing.
Even if I had the added statement that every family has at least 2 kids it makes no difference, though I know you understand by your first post.

Just to make it clear to everyone that this is not the important explanation. (which UR gave)

Imagine 2 families, one with 4 kids the other with 6 kids.
Average family size is 5, but if you ask the 10 kids randomly, 4/10 ull get 4, 6/10 ull get 6, for an average of 5.2....

Its funny how things that appear obvious are not always...

For example a batter in baseball can have a higher average in both half seasons than another batter, but a lower average for the whole season...


BTW a practical bet you can make with ppl that takes advantage of the second question of this thread.

You have 3 cards, on is both sides black, one is both sides red, last is one side red one side black.

You take a random card from a hat, say and look at one side.

Its red, say, so its either the red red or red\black, and he bets even money its red red since there are two choices.

Fair bet?

[Snowflake]

Wow that is a good trick. I guess it is more likely the card you picked is the one with both sides red. Since it is less likely you picked the R/B card and you happen to see the R side.

[Snowflake]

Originally posted by Lul Thyme

For example a batter in baseball can have a higher average in both half seasons than another batter, but a lower average for the whole season...

I don't know baseball at all. Why is this possible?

[Dauphin]

Originally posted by Snowflake


I don't know baseball at all. Why is this possible?

Its Simpsons paradox

I'll let wikipedia fill you in.

http://en.wikipedia.org/wiki/Simpson's_paradox

[Snowflake]

Ahh I see. The key is that the amounts (numbers of at-bats, I suppose) that the avgs apply to are very different.

[Lul Thyme]

It has nothing to do with baseball...

You can have a higher average income per person for white than ppl in 2 countries, but in the two countries together blacks have higher average.

Or whatever example you want, meaning if something has higher average in two populations it might not have higher average in the pooled population.

[Lul Thyme]

BTW dauphin you should correct your link, it has a typo..

[Lul Thyme]

Originally posted by Snowflake
Wow that is a good trick. I guess it is more likely the card you picked is the one with both sides red. Since it is less likely you picked the R/B card and you happen to see the R side.

Yes the odds are 2/3 thats its the double colored card and 1/3 that its the card with different colors...

[Dauphin]

Originally posted by Lul Thyme
BTW dauphin you should correct your link, it has a typo..

Works fine for me.

[KrazyHorse]

Originally posted by Lul Thyme
Yes Krazyhorse.
But thats only part of the thing.
Even if I had the added statement that every family has at least 2 kids it makes no difference, though I know you understand by your first post.

Yes. I also could have said that the answer you get by polling the kids is equal to M+V/M where M is the actual mean and V is the variance...

I was trying to demonstrate as simply as possible the fact that the two are not equal.

[Kuciwalker]

Originally posted by Dauphin


Works fine for me.

If I click the link, it replaces the special characters with lots of ampersands.

[Urban Ranger]

Works for me too

[Snowflake]

Kuci's a little lost lately.

More math problems?

[Mr. Harley]

OK, I get the apparent paradox - giggle, giggle - and we had lots of fun, too. You are pre-eliminating certain conditions, which I should have caught in your original description. I understand why so many mathematicians got it wrong, too. If you've been running plain vanilla multi-variant stats, you never have this kind of situation, in fact because so many experiments are double-blind, you go out of your way to prevent it. Thus many people who have run statistics for real world experiments will try to fit this into the paradigm of standard statistical studies, which it isn't. Yet it's just similiar enough to mislead someone who's been doing it.

[Lul Thyme]

Originally posted by KrazyHorse


Yes. I also could have said that the answer you get by polling the kids is equal to M+V/M where M is the actual mean and V is the variance...

I was trying to demonstrate as simply as possible the fact that the two are not equal.

Yeah but I was afraid some ppl were going to think that orphans or family with no children were somehow to blame for this whole situation and get angry at them or something ...



ok shawn let me try to think of more funny little math tricks and games everybody can understand...