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The instructor calculated the mean and the standard deviation, using the 20 numbers given, and he said that these are the population mean and population standard deviation. Then he calculated the sample mean and sample SD from those values. Is he correct ?

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as long as you meant to say, he used the sampled mean and sd asestimatesof the population mean and sd, then yes - thats a normal thing to do.

The thing you have to realise is that when you take a random sample, you dont know in advance which data will be in the sample. As a result mean of the sample is also a random variable. The question asks you to find:I think the mean and the standard deviation of those 20 number are already the sample mean and sample SD.

"the sd of the sample mean"

not"the sd of the data in one particular sample"

Once you have an estimate of thepopulationstandard deviation, you can estimate the sd of your sample means by writing them as the sum of some random variables

(provided the sample values are independant)

(because all the x values come from the same distribution)