I am confused on a basic statistics concept. Also, my terminology may be a bit off as well; I am a novice. I will be as simple and concise as possible. Hopefully, this scenario gets to the core of my question.

You are in a gym with a lot of basketballs. You are tasked with finding the mean volume of the basketballs in the gym. All you are equipped with is a a ruler and your eyes. Thus, you take multiple measurements of the diameter for each basketball you decide to sample. After your collection, How do you do your estimation? (Volume of a sphere is Volume = 4/3 * pi * r^3)

(a) calculate the mean volume for each basketball measured. Then, use those mean to estimate the population mean.

(b) calculate the volume of the basketball for every measurement. Then, use those numbers to estimate the mean

(c) some other option I haven't thought of

Bonus - Why the choice?

This example is meant to strike to the heart of my question. How would use an estimator, or parameter, for a calculations that you would like to do stats on? Is there a best way to do this? What would be the statistical area that this problem would lie so that I may do additional reading on the topic?

Thank you for your input

  • $\begingroup$ This is an excellent question I don't have time to answer properly but you might want to search bias, consistency, sufficiency, and efficiency as criteria for choosing a statistic (ie estimation method) to make an inference about a parameter. Also, maximum likelihood, minimum variance unbiased estimator would be useful. $\endgroup$ – Peter Ellis Feb 8 '18 at 0:53

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