In other words, If I have correctly understood, if n is sufficiently large (there are various conventions in this sense, for example,

**n>30**or n>100) the sampling distribution will tend to a Gaussian (regardless of the features of the population distribution). But now my doubt is that I have always misunderstood the notion of sampling distribution. In practice, suppose I want to study the height distribution in English males and it doesn't follow a Gaussian distribution. With a sampling distribution with n>30, X≃ (mu, sigma).

But what is meant by sampling distribution, for example with n=30? I meant the sampling distribution like this:

*For example, I have a sample of 3 boys with 3 associated heights: X1=175 cm, X2= 180 cm, X3= 190 cm.*

The sampling distribution then contains all the possible means in this sample: X1+X2+X3/3, X1+X2/2, X1+X3/2, X2+x3/2.

The sampling distribution then contains all the possible means in this sample: X1+X2+X3/3, X1+X2/2, X1+X3/2, X2+x3/2.

Therefore, I had understood that, If I take a sample of at least

**30**people, the distribution that contains all the possible averages within this sample, will tend to a normal distribution, despite the population distribution of English males is not symmetrical (to mention the previous example).

On the other hand, from other online examples, I had interpreted that

**n>30**conventionally required to apply the central limit theorem as "a sample containing

**at least 30 means**of the values of as many samples". So, if I have a sample with a sufficiently large number of n means from n samples, I can approximate the distribution to a normal one.

Would anyone be able to clear my head about n, the sampling distribution and the central limit theorem in general?