Central Limit Theorem with n=1

[Jessica84]

I’m confused about the CLT and I’m not sure if we obtained many samples of lenght 1 (and considered those values the means) , or we used only one mean coming from one sample.

As it stated “the central limit theorem says that the distribution of the sample means coming from many samples, is nearly normal centered at the population mean, with standard error equal to the population standard deviation divided by the square root of the sample size”

During the lab C3_W3_Lab_1_Central_Limit_Theorem, we interacted with utils.gaussian_clt() and we are able to chose different n’s for sample sizes, however, the smallest n number was n=2. Moving ahead in the course, I believe that we used sample sizes of n=1, because in the height explanations the heights were collected from an ‘n’ amount of subjects and then, with those subjects we applied the CLT. Or I don’t know if what happened was that we collected only one sample of size n and we worked with that unique mean.

If is possible to collect many samples of size n and apply the CLT, why does the utils.gaussian_clt() does not allow n=1?

[lucas.coutinho]

Hi @Jessica84!

The video for the CLT has a wrong explanation. The CLT says that, under certain conditions, the value

\frac{X_1 + X_2 + \ldots + X_n}{n} converges to N(\mu,\sigma^2/n), where \mu = E[X_i].

The video mistakenly implies that what converges is the mean of n-uples of samples from X_1, \ldots, X_n.

We are fixing the video to avoid confusion. The function doesn’t alow n = 1 because it means only one observation and it is pointless regarding CLT.

I hope that helps.

Cheers,
Lucas