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What is the most accurate way to estimate the 60th percentile if I know the 75th percentile and the median? No access to underlying data.
How does linear interpolation work in this case?
In linear interpolation, we estimate the value of a percentile between two known percentiles by assuming that the distribution of the data between those percentiles is linear. For example, if the median is the 50th percentile and the 75th percentile is known, we can estimate the value of the 60th percentile by assuming that the values between the 50th and 75th percentiles are distributed linearly. We can then use this assumption to estimate the exact value of the 60th percentile.