Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    13
    ReputationRep:
    I think I misunderstand this. I think it means that if you take enough of the same sized random samples from a population then the means of the samples are distributed normally.

    But supposing that the sample mean happens to be nowhere near the population mean then how does using a sample mean help.

    This question probably makes no sense but that's because I just don't get what's going on in CLT.
    • PS Helper
    • Study Helper
    Offline

    13
    ReputationRep:
    PS Helper
    Study Helper
    (Original post by maggiehodgson)
    I think I misunderstand this. I think it means that if you take enough of the same sized random samples from a population then the means of the samples are distributed normally.

    But supposing that the sample mean happens to be nowhere near the population mean then how does using a sample mean help.

    This question probably makes no sense but that's because I just don't get what's going on in CLT.
    The point is that as you take more and more samples, it gets less and less likely that they're all skewed away from the mean. Some will be skewed in the opposite direction to others, and they'll all average out. The CLT says "whatever you sample, in whatever distribution, if you take enough samples then the mean follows the normal distribution" - that is, if m is the population mean and s the standard deviation of the population, P(a < (Sn-n m)/(sqrt(n) s) < b) tends to phi(b)-phi(a). The square root on the denominator is there because of a reason that I can't convey without sketching, but at A-level (IIRC), that's not important.
    • Thread Starter
    Offline

    13
    ReputationRep:
    Thank you.

    So in the questions where you are told x(bar) is something then that x(bar) in the mean of ALL the sample means not just the mean of one of the samples where it could be quite iffy?
    • PS Helper
    • Study Helper
    Offline

    13
    ReputationRep:
    PS Helper
    Study Helper
    (Original post by maggiehodgson)
    Thank you.

    So in the questions where you are told x(bar) is something then that x(bar) in the mean of ALL the sample means not just the mean of one of the samples where it could be quite iffy?
    It depends on context - the sample means will (nearly) follow the normal distribution, so you end up with a sample from the normal distribution. I can't tell which xbar is without context - if there's more than one of it, then it's the sample means, while if there's just one, then it's the mean of the sample means.
    • Thread Starter
    Offline

    13
    ReputationRep:
    Sitting here banging my head on the desk. I'm just not going to get CLT I think. I will mull over some questions bearing in mind what you've told me and hope that a practical or 12 will help this concept drop into place.

    Thanks very much.
    • PS Helper
    • Study Helper
    Offline

    13
    ReputationRep:
    PS Helper
    Study Helper
    (Original post by maggiehodgson)
    Sitting here banging my head on the desk. I'm just not going to get CLT I think. I will mull over some questions bearing in mind what you've told me and hope that a practical or 12 will help this concept drop into place.

    Thanks very much.
    I can tell you why the CLT is true, if you like (it's not a fully rigorous proof, it relies on MGFs which aren't necessarily defined for all variables) - although if you've not already done a fair bit of probability, it probably will take a while to understand (or even a whale, as I first typed). For me at A-level it just took lots of questions.
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.