in definition of percentile, it is said that, some value is in 30th percentile means, 30 percent of the data values are lower than the given value. But my confusion is, what if I have 1000 data values, which are all 10, then each percentile is same, and no one is smaller or larger than anyone else. why it is not lower or equal? could someone please clarify the concept?
thanks in advance.
There is a convention (seen often in standardized test scores) of $99$ being the highest percentile. Why? Because two people who both received top marks cannot both be in the $100$th percentile. So to answer your question: All of the values in your data set fall into the $99$th percentile, that is, they are the greatest value in the data set. The $30$th percentile is empty, because no datum is smaller than $70$% of the other data.