Ok I've got some context and a definitive question (hopefully)...
(Improving upon https://math.stackexchange.com/questions/1426711/how-to-calculate-percentiles which I'll delete shortly)
I have a working example of how to calculate a value's percentile value within a range of values...
0.00, 0.00, 0.01, 0.30, 1.00, 2.00, 2.00, 2.00 is the range of values (the first data set).
2.00 is the value I need to be finding the "percentile value" of.
The formula is
(((B + (0.5 * E)) / n) * 100) where B = 'number of scores below x', E = 'number of scores equal to x', n = 'number of scores'.
Applying this I get
(((5 + (0.5 * 3)) / 8) * 100) = 81.25%
The percentile value of 2.00 within the above data set is 81.25%.
Now here is the problem / my question:
Given another data set, how do I find the value within it that would have the percentile value of 81.25%. I've found a long way to do it which is to use the method above to find each value's percentile value and then work out how 81.25% corresponds. But this is quite intensive if it is a large set. Is there a quicker and more efficient way to do this? Ie. kind of the reverse of the formula above.
edit/PS: I'm a software developer so forgive my terminology, bad representation of formulas etc. If I need to clarify anything let me know.