# How to calculate percentile rank if all values are equal to zero

The formula for finding Percentile rank as per wikipedia is

One of the edge cases in my application is when all the values are zero. In this case the number of scores less than the score of interest is zero, the frequency is equal to the number of total values which is N.

This formula gives me a rank percentile of 50% when all the scores are equal and zero. It seems counter intuitive to suggest that the rank percentile is 50% even though there is not a single score less or more than the score of interest. Is this the correct value?

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Other possible values would be 0% (if by rank percentile you mean the percent strictly less than) or 100% (if you mean the percent less than or equal to). But ranking is pretty meaningless when all the values are the same, so 50% is as correct as either of the above.

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Thanks!! I was not sure if that was the right answer –  ganeshran Nov 7 '12 at 10:52