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If I take 10 items (a small sample) from a population and calculate the standard deviation, then I take 100 items (larger sample), and calculate the standard deviation, how will my statistics change?
The smaller sample could have a higher, lower or about equal the standard deviation of the larger sample. It's also possible that the smaller sample could be, by chance, closer to the standard deviation of the population. However, A properly taken larger sample will, in general, be a more reliable estimate of the standard deviation of the population than a smaller one.
There are mathematical equations to show this, that in the long run, larger samples provide better estimates. This is generally but not always true.
If your population is changing as you are collecting data, then a very large sample may not be representative as it takes time to collect.
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How do i find sample standard deviation from population standard deviation?
If the population standard deviation is sigma, then the estimate for the sample standard error for a sample of size n, is s = sigma*sqrt[n/(n-1)]
How does one calculate the standard error of the sample mean?
Standard error of the sample mean is calculated dividing the the sample estimate of population standard deviation ("sample standard deviation") by the square root of sample size.
Does the distribution of sample means have a standard deviation that increases with the sample size?
No, it is not.
As the sample size increases the standard deviation of the sampling distribution increases?
No.
What is the standard error if the population standard deviation is 100 and the sample size is 25?
Formula for standard error (SEM) is standard deviation divided by the square root of the sample size, or s/sqrt(n). SEM = 100/sqrt25 = 100/5 = 20.
