Question

If I have the mean and standard deviation of a distribution, but need to find the means and standard deviations from random samples, how would I do this using the Central Limit Theorem?

Answer 1

Central Limit Theorem claims that given a large enough collection of samples, the mean of the sample means will equal (or closely approximate) the population mean.

Answer 2

but if the sizes are different, such as 5, 50 and 150, what should i do?

Answer 3

I'm still a little confused on what you want to accomplish.
So you have 3 samples of sizes 5, 50, and 150 and you want to find the means and standard deviations of them?

Answer 4

exactly, because the original mean is 9.6 and the standard deviation is 8.2. So im trying to find the new values for those random sample sizes

Answer 5

Interesting. That's the reverse of what one usually tries to do.
I would say that if you have the data from those three samples, then just calculate those stats, but I'm guessing that's not the point of this exercise.

You can probably work backwards from things like standard error...

In theory, if the collection method is SRS, then the sample means should equal or be at least be approximately equal to the population mean (precision improves with sample size.)

If you are familiar with standard error, it is a way to use the sample standard deviation to estimate the population standard deviation by dividing by the square-root of the sample size.
Doing that in reverse, you can get the sample standard deviation by multiplying the population std.dev. by √n.

Answer 6

The original data only provides, the mean, standard deviation and a histogram. would i still work backwards and use standard error?

Answer 7

I'm not sure how else to do it. I hope I'm not getting the formula backwards.
Check this to make sure it is relevant to what you're doing:
http://stattrek.com/sampling/sampling-distribution.aspx

How does that histogram look? Does it look approximately normal?

Answer 8

the histogram is rightly skewed and unimodal, with possible outliers at the end

Answer 9

Hmm, and that's a population histogram, or is it for one of the samples?

Answer 10

its a population one. it was for the previous exercise, and this is the one following.

Answer 11

in that case, I wouldn't even bother with the sample of size 5, that is too small to tell you anything; the others should have equal means and standard deviations = σ/√n

Answer 12

their means and standard deviations should be equal to the standard error i calculate then?

Answer 13

Yes, as far as I can tell you now. Like I said, this is backwards from what I usually see with sampling distributions.

Answer 14

Okay, and I just have one more question i promise! what does it mean when they ask, comment on if the values agree with the distribution?