I'm currently reviewing for my final exams tomorrow, and I still don't get how to solve the required quantities using this consideration to find the variance, standard deviation, and coefficient of variation:
considering this set of values as a sample of all possible measurements of this dimension.
Other than the one above, I can solve with this consideration:
considering this set of values as a complete population.
Some of the exercises I have on hand have these two considerations, so it would be a big progress if I learn how to interpret the first one mentioned above.
Some notes
Here's the set I was given.
{21.14, 21.37, 21.53, 21.61, 21.87, 21.93} units in mm
I currently have the following
mean = 21.575 mm
median = 21.57 mm
If you've seen my previous questions, once again, I don't need the solution. I need the interpretation.
I would interpret the first consideration as saying that you need to use sample-based descriptive statistics while in the second case you assume that the data given fully specify the distribution of possible values so you would use population-based descriptive statistics.
Specifically, the formula for a population mean and sample mean are the same, as is the formula for the sample or population medians. The only one that technically is different is the sample variance vs. the population variance (the latter being smaller by the factor $\frac{N-1}{N}$).
Now, since you said "Descriptive" statistics, that is all there is to it. However, if you are trying to infer the population-based value from a sample, then you need to assume some underlying distribution for your data and then decide what estimation scheme you want to use (e.g., Maximum Likelihood, Method of Moments, Bayesian estimation).
Hope that helps.