How do I quantify rank/percentile? Known: Min, Max, Median, Avg & Total Count

Hello All,

I have a problem where I have a value that I want to rank or assign a percentile.

I do not know all individual values that comprise the data set I am comparing to, but I do know the overall count. Example Scenario:

Value I want to rank: 57

Values to compare to
Total Count: 11
MIN: 34
MAX: 99
MEDIAN: 56
AVG: 67

Is there a function or formula (or technique) I could use to provide a value that explains my value of 57, relative to the overall group of 11?

Thanks in advance for any ideas!

HiShg,

I'm really interested in these two items:

Rank.

If I knew all 11 values, I could say in the series of [34,38,53,54,55,56,57,96,97,98,99] my value of 57 is in 7th position (smallest-to-largest) or 5th position (largest-to-smallest).

Percentile.

If I knew all 11 values, I could use the PERCENTRANK.EXC function and provide a decile value for my 57, 58th percentile (largest to smallest) and 42nd if reversed (smallest to largest).

My question is, is there a way to manufacture something similar, understanding it is an estimate, when all 11 values are not known.
Instead, we have the total range defined by the MIN and MAX, our value which is inclusive to the data, the overall average, and the Median (which could be our value in some cases).

Any thoughts or best practices how to handle this problem with incomplete data for the whole set?

Thanks!