# How to efficiently determine the number of samples required for a given statistic?

Articles often claim percentages such as "46.1%" for some statistic. In this case, one can tell that they definitely had more than two measurement points, otherwise the statistic would have been either 0%, 50% or 100%.

Using brute force, I made a tool that will figure out the answer. In this particular case, there is only one result that will lead to 46.0512%, which is 414/899 (for just 46.1%, there are multiple smaller solutions).

Is there a method, more efficient than brute force, to find possible inputs that lead to this result? Or find the lower bound for either the numerator or denominator?

• Yes I understand what you would like to get, but I don't think you can get anything meaningful. Look at how you can approximate $\pi$ for example with many rational forms 22/7, 201/64, 355/113 and observe how close these numbers are. – ippiki-ookami Aug 24 '18 at 7:24