For example, a test was given to a class of 5 students, and the test results are 12, 55, 74, 79 and 90.
Mean (μ) = ΣX/N, where Σ is the summation (addition) sign, xi is each individual number, and N is the population size. In the case above, the mean μ is simply (12+55+74+79+90)/5 = 62.
For the example given, the standard deviation is sqrt[((12-62)^2 + (55-62)^2 + (74-62)^2 + (79-62)^2 + (90-62)^2)/(5)] = 27. 4. (Note that if this was the sample standard deviation, you would divide by n-1, the sample size minus 1. )
So for the example above, if this were a sampling of 5 students from a class of 50 and the 50 students had a standard deviation of 17 (σ = 21), the standard error = 17/sqrt(5) = 7. 6.
