You have found the mean to be:
So, the standard deviation is:
Where N is the number of elements in the population, is the i-th element in the set, and is the mean.
And there you go.
A population consists of the five numbers 2,3,6,8 and 11. Consider all possible samples of 2 that can be drawn with replacement from this population (i.e. as soon as soon as number has been drawn and its value noted it is replaced and can be drawn again). Find
i) The mean of the population.
ii) The standard deviation of the population.
iii) The mean of the sampling distibution of means.
iv) The standard deviation of the sampling distribution of means.
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For i) I calculated the mean to be 6.0 however I found the standard deviation for part ii) to be 3.67 to which I am unsure of its reliability.
Can anyone please help with these please, I am keen to learn the method to solving these.
Regards
For (iii) and (iv) read this: Sampling distribution - Wikipedia, the free encyclopedia
Thanks, for the input Aryth, that was very helpful.
Is the standard deviation not...
And is the standard deviation of
Thereby meaning the standard deviation is not 3.29 but 1.47?
I'm lost, can you please untangle this mess?
Thanks
Mr Fantastic, I can't understand how to apply the math on that wiki article. Kind Regards,
Ross
This is an unbiased estimator and is used to estimate the sd of a population from a sample taken from the population. You have only a sample (no mention of where it's come from) and you want the sd of only the sample. So the original formula you were given is the one to use.