# Population Mean, Population Standard Deviation, and z-scores

#### bengalgirl

##### New Member
Hello!

My stats teacher gave me a problem with a list of 20 numbers:
1000, 1290, 1290, 1200, 1460, 1410, 1320, 1300, 1290, 1150, 1300, 1600, 1080, 1360, 1110, 940, 1200, 1430, 1410, 1060

She then told us to find the population mean and the population standard deviation so that we could calculate the z-scores of several other numbers.
I understand how to calculate the z-score of a number. But how is population mean different from regular mean and how is population standard deviation different from just standard deviation?
Will they be different numbers than the regular mean and standard deviation? If they are different, how do I calculate them? Can I calculate them using R or do I have to do it by hand?

I have the regular mean as 1260 and the regular standard deviation as 28063.158, but with these numbers my z-scores do not make sense. An explanation would be greatly appreciated! Thanks!

#### ArtK

##### New Member
Double problem here. The 28,063 is a variance. But it's a sample variance.
You divided by 19 instead of 20. So find the population variance and take
the square root to have the (population) standard deviation (sigma). You
have the population mean ok.