Mathematics of data management - standard deviation?

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!!!

Mean= E[X] =(Total number of hours)/(total number of people) =
=(12*1+ 32*5+35*7+ 38*8+ 42*5)/(1+5 +7+8+5) = 35.8

Variance = E[X^2]-[EX]^2=
(12^2*1+ 32^2*5+35^2*7+ 38^2*8+ 42^2*5)/(1+5 +7+8+5) - (35.8)^2 = 33.6

deviation = (variance)^(1/2) = (33.6)^(1/2) = 5.8

The previous answerer did not answer the asker's first question:
The sample standard deviation is an estimate of the population's standard deviation. When the sample size is small (n < 30) the estimate is not considered very good and statistical problems are solved, using the t-distribution to compensate.
If the sample size is 鈮?30, and/or if the population standard deviation is known, the z-distribution is used.