For a distribution, let's say I know the scores at the 10th, 30th, 50th, 70th and 90th percentiles. I also know the interquartile range and range. Is it possible to get the exact percentile rank of a given score? I'll be using R if that makes things any easier.
As a more concrete example, I have the following information:
Lowest: 5.10, Highest: 6.00, iqr=0.12
10% <= 5.25 30% <= 5.71 50% <= 5.84 70% <= 5.95 90% <= 5.96
Let's say I want to know the percentile rank of the score 5.33. I can see that it's somewhere between 10 and 30. Is there a way to calculate this outright, or maybe somehow I can recreate (estimate) the distribution based on those percentiles and estimate it that way?