Estimating a sample mean from population data.

B

Bobstradamous

Guest
#1
All,
Thanks for taking the time to read this thread. If I am given information about the population (population mean and standard deviation), can I determine the approximate mean for a randomly drawn sample (if the only information I am given about the sample is the sample size)? For example, if I am told the population mean is 67 and the population standard deviation is 16, can I determine the mean for a randomly drawn sample with 64 draws (if the numerical value for each of the draws is not listed)? Thanks. Bob
 
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A

ab-stats

Guest
#2
There is no way to determine the exact mean of a random sample without at least knowing the sum of the measurements, but if the population mean and standard deviation are known, it's possible to derive the sampling distribution. The expected value (in other words, the mean of all possible sample means) will be the same as the population mean. And the standard deviation of the sample mean itself will be sd/sqrt(n). As n grows very large, then the sampling distribution will be approximately normal.