# Thread: variance of sample mean and sample standard deviation

1. ## variance of sample mean and sample standard deviation

Hi all!

I would like to know how to derive the expected variance of sample mean values and sample standard deviation.
(I am not a statistician so please forgive my sparse use of formulas.)

I have the following scenario:
1. 10 drawings from a normal distribution (M=0; SD = 1)
2a. Calculate the mean valure from these 10 drawings.
2b. Calculate the standard deviation from these 10 drawings.
3. Repeat steps 1 and 2.

Now, I would like to know the expectancy values for the standard deviation of the mean values from 2a and the standard deviation from 2b.

For the mean, it is simply SDm=((mean/sqrt(10)))^0.5

For the standard deviation, my current suggestion is:
SDsd = sqrt(0.18)^0.5

0.18 -> based on the sample variance distribution for N = 10 in a normal distribution
(Sample Variance Distribution -- from Wolfram MathWorld)

So, do my considerations make sense?

Also, in more general terms: I wonder if it is correct that the estimated standard deviation is lower for mean values than for standard deviations, since SDm > SDsd for all N.
In other words: Estimations of the standard deviation of the standard deviations are more precise than estimations of the standard deviation of sample means!?

thanks in advance for your help!

trantor

2. Hi there

Sorry but I am not clear on the question. Is the question

1. draw 10 values from a N(0,1)
2. calc mean and var
3. draw 10 values from N(mean,var) where mean and var are from step 2?

Thanks

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