Maths of Data Management?

Hi to everyone! I really need help, I am so confused with finding varience and standard devitiation...
My first question - can you please explain me when do we use population standart deviation and sample standard deviation? Can you please give some examples so I could understand the concept.
My second question is help me to solve the problem according to what I asked before...
Here is the problem:
Thde nurses` union collects data on the hours worked by operating-room nurses at the Hospital.
There are two columns:
Hours per Week Numbers of employees
12 1
32 5
35 7
38 8
42 5
Determine the mean, variance, and standard deviation for the nurses` hours. Please explain how you solve it, because I already have answers : mean - 35.8; variance - 33.6, deviation-5.8... Thanks in advance. If you help me, I will give you 10 points!!!

Make a third col = C1 x C2, e.g. 12 x1 = 12 etc
Make a 4th col = C1 x C3 = 12 x 12 = 144
Total cols 2 - 4
Mean = tot col3/tot col 2
SD = tot col 4/tot col 2 - mean ^2

mean is just the sum of all the data divided by the number of data so it is (12.1+32.5+35.7+38.8+42.5)/5
the variance is the sum of the mean minus each peice of data squared and then divided by 1 less than the number of data (you add up all values of ("mean x"-x)^2 and then divide by 4
the standad deviation is just the square root of the variance.