And, at least in my head, when I think of the trials as you take a sample size of 16, you average it, that's the one trial, and then you plot We plot our average. Melde dich an, um unangemessene Inhalte zu melden. The standard error is an estimate of the standard deviation of a statistic.

We take a hundred instances of this random variable, average them, plot it. But to really make the point that you don't have to have a normal distribution I like to use crazy ones. Schließen Ja, ich möchte sie behalten Rückgängig machen Schließen Dieses Video ist nicht verfügbar. The standard error is a measure of variability, not a measure of central tendency.

So it's going to be a very low standard deviation. The means of samples of size n, randomly drawn from a normally distributed source population, belong to a normally distributed sampling distribution whose overall mean is equal to the mean of Wird verarbeitet... III.

So we take 10 instances of this random variable, average them out, and then plot our average. That's why this is confusing because you use the word mean and sample over and over again. Now I know what you're saying. And let me take an n of-- let me take two things that's easy to take the square root of because we're looking at standard deviations.

Naturally, the value of a statistic may vary from one sample to the next. So 9.3 divided by 4. Melde dich an, um dieses Video zur Playlist "Später ansehen" hinzuzufügen. And actually it turns out it's about as simple as possible.

We're not going to-- maybe I can't hope to get the exact number rounded or whatever. Here we would take 9.3-- so let me draw a little line here. The difference between the means of two samples, A andB, both randomly drawn from the same normally distributed source population, belongs to a normally distributed sampling distribution whose overall mean is Let's do another 10,000.

So we've seen multiple times you take samples from this crazy distribution. So let's say you were to take samples of n is equal to 10. But let's say we eventually-- all of our samples we get a lot of averages that are there that stacks up, that stacks up there, and eventually will approach something that Wird geladen...

So if I know the standard deviation-- so this is my standard deviation of just my original probability density function, this is the mean of my original probability density function. I take 16 samples as described by this probability density function-- or 25 now, plot it down here. It'd be perfect only if n was infinity. But even more important here or I guess even more obviously to us, we saw that in the experiment it's going to have a lower standard deviation.

You know, sometimes this can get confusing because you are taking samples of averages based on samples. Wird verarbeitet... The Greek letter Mu is our true mean. Here we're going to do 25 at a time and then average them.

Anmelden 55 7 Dieses Video gefällt dir nicht? Let's see. So this is the variance of our original distribution. This isn't an estimate.

So I'm taking 16 samples, plot it there. It's one of those magical things about mathematics. n equal 10 is not going to be a perfect normal distribution but it's going to be close. Specifically, the standard error equations use p in place of P, and s in place of σ.

Wird geladen... But anyway, the point of this video, is there any way to figure out this variance given the variance of the original distribution and your n? Sampling distributionsSample meansCentral limit theoremSampling distribution of the sample meanSampling distribution of the sample mean 2Standard error of the meanSampling distribution example problemConfidence interval 1Difference of sample means distributionCurrent time:0:00Total duration:15:150 All of these things that I just mentioned, they all just mean the standard deviation of the sampling distribution of the sample mean.

And then I like to go back to this. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.