I don't know if I'm allowed to quote from your study notes, I'm really sorry if I am not.

"Let’s take the following series: 10, 12, 14, and 16. The average of the series is (10+12+14+16) / 4 = 13. So, for the population variance, in the numerator we want to sum the squared differences. The population variance is given by [(10-13)^2 + (12-13)^2 + (14-13)^2 + (16-13)^2] / 4 = 20 / 4 = 5. The sample variance has the same numerator and (4-1) for the denominator: 20 / 3 = 6.7."

My question is how do you solve for the sample variance using the Var(x)=[E(X^2)-E(X)^2] formula.

I tried calculating for the population variance (as shown below) and it worked, but how do you do it for the sample variance? Where would the (n-1) part come into the equation? Thank you very much!

Var(pop)=[(10^2+12^2+14^2+16^2)/4]-13^2 = 174-169 = 5