Central Limit Theorem

[@aybay8723]

Beautifully explained mate

[@farhimouad2860]

thank you. but you do not mention the importance of the sample size??

[@lastua8562]

usually +35 to get a normal distribution in most cases.

[@cateattingmonster0]

If all the population samples are positive, using sampling and by the central limit theorem is it possible to graph the normal distribution curve? Because samples are all positives, the normal curve will be just positive side only and no negative side of the curve can be drown at all correct?

[@farhimouad2860]

+cooky the normal is centred arround the mean and not arround zero. if you standartize it it will be centered arround 0 (z distribution)

[@haroldbaker555]

My brain is going to explode

[@lastua8562]

In the **Population**, if it is uniformly distributed, why are we still able to draw inference about the population using our sample?

[@kenkrak4649]

does this work with samples with a size of N=1?

[@lastua8562]

no.

[@ahmadghaemi2192]

If the population consists exclusively of mu, then the sample cannot be uniformly distributed, right? Is there a condition being violated there?

[@lastua8562]

if all observations are mu, then you cannot draw inference. A uniform distribution is obtained by rolling a die

[@ahmadghaemi2192]

​@@lastua8562 by definition? where have you seen that? I can't find anything on it online.

[@lastua8562]

@@ahmadghaemi2192 "if the population consists exclusively of mu" - this means you have 100 students who are all 1.80m. If you take 10 of them, all of them will be 1.80m, and you don't have variation. "The sample cannot be uniformly distributed, right?" - a sample will always be normally distributed, not uniformly.

[@ahmadghaemi2192]

​@@lastua8562 Thanks for your answers. Yes, I meant normal distribution. So you mean that the condition is that there exists variation in the population. If there are only two values in the population, then CLT will hold I guess. I could see that.

[@lastua8562]

@@ahmadghaemi2192 no. if there are only two values in the population, you cannot draw a sample from it. You need 35 or more observations in the SAMPLE for the CLT to hold, on average.