AP wrote:
>
> Hi all:
>
> I would appreciate your help in solving this question.
>
> calculate the standard deviation of a sample where the mean and
> standard deviation from the process are provided?
> E.g. Process mean = 150; standard deviation = 20. What is the SD for
> a sample of 25? The answer suggested is 4.0
Right answer, wrong question...
You were, almost certainly, not asked for the standard deviation of the
sample, but for the standard deviation of the MEAN of the sample.
The thing you need to note here is that the sample is obtained through
a random process, so that most things computed from the sample are
likewise randomized through the sampling process.
It is often helpful to think of taking a lot of samples all of the same
size, computing the mean (or whatever) for each of them, and then
analyzing that set of numbers. In particular, you can calculate the
standard deviation.
Probability theory tells us that in the population of ALL samples of
size N from a population with mean mu and standard deviation sigma, the
sample means will have mean mu and standard deviation sigma/sqrt(N).
Moreover, as N gets larger, the "sampling distribution" gets closer to a
normal distribution, which under some circumstances lets us say more
about the distribution based on mu and sigma/sqrt(N).
-Robert Dawson
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