Central Limits Theorem :/ (project maths HL)

cocopopsxx

Hey,
I don't get the Central Limits Theorem at all at all and haven't a clue how to do that hourly earnings question in the exam papers (2012 SEC sample paper Q7 part (b) ). I don't get the question or this theorem at all. Can anyone tell me the point of it...or of project maths...or of it's existence? :mad:

I'm screwed for paper two, trig has never been my thing, the first six questions are grand and I thought probability and statistics questions will be okay too until this meanie- The Central Limits Theroem- creeped up. HELPP?

reznov

I don't think we need to learn a Central Limit Theorem in probability. Are you sure it is not deferred material!

Canard

It actually is on the course...I was at a revision course and the guys running it said there was a lot of confusion but that its on this year.

I dont know much about it other than it states "The mean of a random sample has a sampling distribution whose shape can be approximated by a Normal model. The larger the sample, the better the approximation will be". It doesnt make a lot of sense to me either.

How would it be used in a question though? I'm looking at SEC 2011 Sample 7b and its about a bike race.

cocopopsxx

reznov wrote: »

I don't think we need to learn a Central Limit Theorem in probability. Are you sure it is not deferred material!

Yes, I am pretty sure. My teacher said that there was uncertainty and confusion about it before so none of the teachers did it but last month, at an inservice, it was made clear that it is on this year so my teacher did it with us last week but I still don't get it.

cocopopsxx

Patchy~ wrote: »

It actually is on the course...I was at a revision course and the guys running it said there was a lot of confusion but that its on this year.

I dont know much about it other than it states "The mean of a random sample has a sampling distribution whose shape can be approximated by a Normal model. The larger the sample, the better the approximation will be". It doesnt make a lot of sense to me either.

How would it be used in a question though? I'm looking at SEC 2011 Sample 7b and its about a bike race.

Sorry, it's 2012 sample! Changed it, so sorry!

Yeah, that's all I know too and two formulae but they don't make sense. I could learn them off but how are we supposed to use it in the question, I wouldn't ever get it!

FaoiSin

What part of the course is this? Is it in the book? "/

Chuchoter

I've never heard of this thing before
Also, I'm looking at this question and I don't see how its relevant anyway.

cocopopsxx

YeaaahFaoiSin wrote: »

What part of the course is this? Is it in the book? "/

Probability and Statistics. Can't see it in the book I have (New Concise Maths 4&5)

Chuchoter wrote: »

I've never heard of this thing before
Also, I'm looking at this question and I don't see how its relevant anyway.

My teacher said that partS of this question is done using the central limits theorem He even did it for us but I don't get it.

Chuchoter

Tbh, I wouldn't worry about it. If it was only last month and its on the paper, it'll be one of these things where you get marks for writing anything

FaoiSin

Sure feck it what's the chances it'll come up

Wesc.

This is how I'd do it:

The lower quartile is 12.80... which is the number in the question. So, 1/4 of the population earn less and 3/4 of the population earn more.

You can use bernoulli trials! Where:
--- n (the sample size) is 6
--- r (number of successes) is 4
--- p (probability of success) is 3/4
--- q (probability of failure) is 1/4

So just plug those figures into the formula and there's your answer!

FaoiSin

Wesc. wrote: »

This is how I'd do it:

The lower quartile is 12.80... which is the number in the question. So, 1/4 of the population earn less and 3/4 of the population earn more.

You can use bernoulli trials! Where:
--- n (the sample size) is 6
--- r (number of successes) is 4
--- p (probability of success) is 3/4
--- q (probability of failure) is 1/4

So just plug those figures into the formula and there's your answer!

It's the later parts that are troublesome "/

Wesc.

YeaaahFaoiSin wrote: »

It's the later parts that are troublesome "/

I've never done anything like that in my life...but here's a link to e-xamit if it's helpful:
http://www.e-xamit.ie/tutorial.php?id=38555&prep=38554&soln=38555&tip=38556&port=38582

FaoiSin

It really amazes me how well they were prepared to implement Project Maths

finality

Had a class on this yesterday. Basically, when you split a population into lots of smaller groups of equal size, if you get the mean of all their means, it will equal the mean of the whole group.

Also, their means will be normally distributed. However, the standard deviation of the means of these groups from the mean of their means is different to the overall standard deviation.

standard deviation of these means = overall standard deviation divided by the square root of the sample size.

And that's all you need to know about the central limits theorem

Hayezer

It is on the course, my teacher had never seen it before but my grinds teacher assured is that it is on the course its just that there was alot of controversy around it. With this, he said it's EXTREMELY unlikely to come up, and if it did there would be uproar.

What finality said. So basically in the 2012 SEC question: Population mean wages:$22.05 . So the sample means are also $22.05 . I don't really get it either, all I know is that the means are equal, and to get the sample standard deviation you use the standard deviation they give you and put it over square root n (It's in log tables)

ChemHickey

Hayezer wrote: »

It is on the course, my teacher had never seen it before but my grinds teacher assured is that it is on the course its just that there was alot of controversy around it. With this, he said it's EXTREMELY unlikely to come up, and if it did there would be uproar.

What finality said. So basically in the 2012 SEC question: Population mean wages:$22.05 . So the sample means are also $22.05 . I don't really get it either, all I know is that the means are equal, and to get the sample standard deviation you use the standard deviation they give you and put it over square root n (It's in log tables)

I've not much time for explaining it atm.

The mean of an extremely large sample is very hard to obtain. Trying to take the average of wages of workers in Ireland (there could be some unaccounted for workers etc.)

So, when getting the mean of an extremely large sample, it is easier to find the approximate value of the mean by obtaining the mean of smaller samples of the larger group.

By getting the mean of the smaller groups and then getting the mean of the mean of the samples taken, it would be approximately the same as getting the mean of the original sample.

The same applies to the standard deviation, except, with standard deviations, the sample is extremely large. Having a large sample means there is a higher chance of error to occur.

To account for this error, you divide by the root of the sample size. this allows for the error as it does in hypothesis testing.

My teacher has been teaching maths and chemistry for ages, retired there but stayed back to teach us and she says it's extremely likely to be up due to the census and elections.

She said it's been ages since it was on the course and that it is back again.

Canard

That actually kinda makes sense, thanks ChemHickey!

If all else fails I'll just write that :L