If I have a set of data such as 3500,4500,5700,7100 that represent the 25th, 50th, 75th, the 90th percentile how would I go about finding a percentile in between two of the given points? For instance, how do I find the best approximation of the 35th percentile? N = 3000
THANK YOU!
You're trying to interpolate the distribution between the given points, which is difficult if you know nothing about the underlying distribution of your data. And especially since you only have 4 points to work with.
If you assume that the distribution is fairly smooth, then the best you're likely to do is just apply a linear interpolation - that is, draw a straight line between the two points and work out the position of the point between them.
For example, if I wanted to estimate the 4th decile, and hence the 40th percentile, I'd be looking for a point between the 25th and 50th percentiles. The line that joins (.25, 3500) and (.5, 4500) is q = 2500 + 4000p, so for p = .4 we have q = 4100.