Mathematics 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!!!

12 1
32 5
35 7
38 8
42 5
Determine the mean, variance, and standard deviation for the nurses` hours.
32 5
35 7
38 8
42 5

~~~~~~~~~~~~~~~
Mean is the average of the n observations.
Here, you need the total of hours divide the number of employess.
Number of hours,12x1 + 32x5 + 35x7 + 38x8 + 42x5 = 931
Number of employees, 1 + 5 + 7 + 8 + 5 = 26
Mean = 931/26 =35.8
~~~~~~~~~~~~~~~~~~~~~~~~~~
variance is s^2 or the standard deviation to the 2nd power.
So the idea is figuring out the standard deviation.
You have the mean, you use the individual to minus the mean, gives us,
(12 32 32 32 32 32 35 35 35 35 35 35 35 38 38 38 38 38 38 38 38 42 42 42 42 42)- 35.8 =
-23.8 -3.8 -3.8 -3.8 -3.8 -3.8 -.8 -.8 -.8 -.8 -.8 -.8 -.8 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 6.2 6.2 6.2 6.2 6.2
You square each of them, you get,
566.44 14.44 14.44 14.44 14.44 14.44 .64 .64 .64 .64 .64 .64 .64 4.84 4.84 4.84 4.84 4.84 4.84 4.84 4.84 38.44 38.44 38.44 38.44 38.44
Then you add them up
about 874.64
874.64/n-1 = 874.64/ 26-1 = 874.64/ 25 = 34.962
sqrt 34.962 will get you the standard deviation or 5.913
Standard deviation = 5.9
~~~~~~~~~~~~~~~
Variance is just standard deviation to the 2nd power or 5.9^2 = 5.9x5.9 = 34.81


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