Central Limit Theorem

For what is probably a fairly easy idea I just don't get it. I've read the section in my text book so many times but the central limit theorem still confuses me. Is anyone able to explain it simpley in terms of what I need to know for S1.
Matt

Reply 1

HaNzY

S1????? i have never heard of the central limit theorem, oh my god, what the hell is it?! panicking now, i knew our teacher hadn't taught us properly! help me too please!

Reply 2

ashy

I only did Central Limit Theorem this year (2nd year degree) - I never did it for S1 :p:

I still don't know it :ninja:

Reply 3

mattplaysbass

this really doesn't look good, it comes up in the past papers, only in 1 markers but still the mark schemes only require single sentances but still it seems like easy marks if I could understand this.

Reply 4

HaNzY

i'm sincerely hoping that that means i don't have to know it, i've never come across it before, not even in the books so i hope i don't need to know it. all i know about normal distributions is standardising, confidence intervals and some other general points that you need to know.

Reply 5

DeWale

Well i do Pure Stats and we have to know about CLT but it's not really anything to important, it's just a theory that might help you with other topics such as the normal distribution. I would just state that "When a random sample size of n is drawn from a population with mean (miu) and variance (variance sign) the distribution of sample means is approximately normal with mean (miu) and variance (variance sign over n)"

Reply 6

mattplaysbass

Theres a sections in my texts book "Statistics S1 for AQA", has a picture of a lightbulb on the front. There are questions on it in the past papers so...... this blows because its probably really easy if someone could explain it better than my text book

Reply 7

mattplaysbass

ok like example from the January 05'
Q. State why, in part (a) (constructing a confidence interval), use of the central limit theorem was not necessary?

A. Volume is normally distributed

So i guess would anyone beable to explain CLT in terms of tat question, thanks for the replies guys

Reply 8

DeWale

Try a mark scheme :s-smilie:

Textbooks can really suck sometimes

Reply 9

HaNzY

i think...something to do with the parent population right, something to do with it not looking like a normal distribution so you gotta use this CLT to find out whether it is. but some things you know are definitely normal e.g heights. thats what i'm getting the gist of atm. and so if you know its normal, why bother with CLT.

Reply 10

HaNzY

This makes some sense to me that i've just found....

The Central Limit Theorem

A very important and useful concept in statistics is the Central Limit Theorem. There are essentially three things we want to learn about any distribution: 1) The location of its center; 2) its width, 3) and how it is distributed. The central limit theorem helps us approximate all three.

Central Limit Theorem: As sample size increases, the sampling distribution of sample means approaches that of a normal distribution with a mean the same as the population and a standard deviation equal to the standard deviation of the population divided by the square root of n (the sample size).

Stated another way, if you draw simple random samples (SRS) of size n from any population whatsoever with mean (mu) and finite standard deviation (omega), when n is large, the sampling distribution of the sample means (Xbar)is close to a normal distribution with mean (mu) and standard deviation (omega/ square root of (n). This normal distribution is often denoted by: N(mu, omega / square root of (n)).