Statistics: Samples vs. Populations

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Statistics
In your opinion can you explain the difference between a population and sample and why do we normally study a sample than a population?

Provide a brief discussion of the following. Include examples in you response to enhance my understanding: systematic sample; stratified sample; weighted mean; standard deviation; mutually exclusive events; independent events; and expected value
Solution:
Samples and populations:

Statisticians carry on endlessly about two particular terms - 'population' and
'sample'. There is in fact good reason for the emphasis placed on these concepts
and we need to be clear about the distinction.

Population

One of the hall-marks of good research is that there should be a clear definition of the
target group of individuals (or objects) about whom we are aiming to draw a
conclusion. The term 'population' is used to cover all the individuals who fall within that target group. The experimenter can define the target group as widely or narrowly
as they see fit. Some experiments may be very general, with the intention that our
conclusions should be applicable to the entire human race or all the cats or all the dogs
on the planet. In other cases, the target may be much more narrowly defined; perhaps
all the females aged 55-65 with moderate to severe rheumatoid-arthritis, living in
North America. The size of the population will vary accordingly. At one extreme (all
humans) there might be 6000 million of them, whereas the group with arthritis
(defined above) might contain only a few million.

Population
The complete collection of individual's about whom we wish to draw some conclusion.

While the sizes of populations may vary, they all tend to be too large for us to be able
to study them in their entirety. Of course, it is possible to define a population so
tightly that the numbers become ...