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I have a single JavaScript benchmark test that I run a number of times and store the results in an array.

I then calculate the mean, variance, and standard deviation of the results of the runs.

My question is do I use formulas for the population or sample?

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  • $\begingroup$ I do not understand the question. See What is the difference between a population and a sample?. What do you think is the formula for the mean of a population ? $\endgroup$
    – steffen
    Commented Jan 22, 2012 at 10:24
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    $\begingroup$ I would treat the results as a sample of a population of an infinite number of runs, but I would like to double check which is why I posted the question. If the runs are treated as a population it affects the notation I use when discussing the formulas (big N for population size vs. little n for sample size) as well as the formula for variance (divided by N for population vs. divided by n - 1 for sample). $\endgroup$
    – John-David Dalton
    Commented Jan 22, 2012 at 17:26

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Since you certainly do not know all possible values of this unknown distribution/population, you cannot calculate it's true properties. The only thing you have is a sample, no matter how many tests you run. If you run the test an billion number of times, your estimated properties are converging to the true values, but an error will still remain (maybe at the 100th decimal position, but it is there).

You can claim, that your sample is identical to the population, but to make such a statement you have to know the population which makes the drawing of the sample obsolete.

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  • $\begingroup$ (+1) As a point of clarification--because it is of independent interest--note that the precision of estimates from a random sample typically scales with the inverse square root of the sample size. Accordingly, a billion tests (of, say, a binary attribute) will give you a solid sense of the first four significant digits but the fifth will still be somewhat in doubt. $\endgroup$
    – whuber ♦
    Commented Jan 23, 2012 at 14:33
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    $\begingroup$ @whuber thank you, of course you are correct. I admit I made the numbers up ... shame on me, I should have known better ! $\endgroup$
    – steffen
    Commented Jan 23, 2012 at 15:25
  • $\begingroup$ No shame at all--just a little literary license. :-) Thank you for offering your helpful reply. $\endgroup$
    – whuber ♦
    Commented Jan 23, 2012 at 15:31
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population is a general components of a study i.e the scores of a students in a class. sample is one or two items drawn from the components in the population which give general view from the results.

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