When trying to calculate the standard deviation of the variance, do I calculate both the population and the sample variance and provide both deviations?

Question

ciarán95 · Answer

Hi @emguy511 ! I'm not sure what the particular question you're dealing with is, but generally when dealing with statistics problems we don't know the true value of population parameters such as the mean (mew) or variance (sigma)

Therefore, we would usually take an unbiased sample of the population, calculate the sample variance (called 'sigma hat') and use this to 'infer' to the population. So, the sample variance is essentially an estimation of the true population variance, which is unknown.

So, what I would say is:
- If you can calculate the population variance, then do so and just report that. You don't need to do any inference in this case.
- If you can't (as will usually be the case), just report the sample variance as an estimate of the the population variance.

Hope that helps you out! :)

emguy511 · Answer

I appreciate your response!  I guess where I am getting myself tripped up is--for the specific question I was given two sample data sets with means of 43 and 44.  I calculated the SS to be 140 and 480.  At this point, I don't know whether to use N or n-1 to provide the standard deviation.

emguy511 · Answer

Also when specifically given (n=8) for example in a question, does it mean that you automatically do your calculations based on the sample variance and standard deviation only when it asks to give the computational and definitional formulas?

jim_thompson5910 · Answer

If all you care about is the collection of values you already sampled, and nothing else, then you use a population variance (population standard deviation). However, in most of statistics, the whole point of statistics is to have a sample representative of the population. You then use the sample to figure out the population at large. Much of the time you won't know the population parameters. It's too costly to figure them out. So you'll resort to using a sample statistic (sample standard deviation or sample variance)

Unfortunately without knowing the full problem, it's not possible to say 100%. However I have a feeling that you'll use the sample versions (instead of the population versions) of each.

emguy511 · Answer

Thank you, Jim!  That was helpful!

For instance, if the question were something similar to this: if I were to say that I measured the frequency that people in Los Angeles exercise at a gym in a year, and asked 5 men with answers = (58, 104, 364, 48, 208) and 5 women (52, 312, 24, 260, 104)? Figure the means and standard deviations for the men and women.

 What would I provide for the actual answer?  Given that specific information, would I just calculate the sample variance and it's standard deviation or also calculate the population variance and deviation?  I'm trying to figure out if I need to include both in my answer or if it would make the answer wrong by doing so?

  I'm also afraid I may just be misunderstanding everything I am trying to learn this week! :)  Thank you so much for your help!

jim_thompson5910 · Answer

It sounds like you're doing a study about the differences between men and women when it comes to going to the gym. 

You would use the sample standard deviation and sample variance. You have sample of 5 people (from each gender) which represent a broader population. If you could ask EVERY member of the population, then you'd use population standard deviation and population variance. However, that's very infeasible. So it's better to go with sample statistics instead.

emguy511 · Answer

Great!  Thanks so much!  That makes complete sense!