What rules are available for deciding which quantile a particular value would fall into when the boundaries of more than one quantile are identical?
My data set includes score ranging between 1 and 20. As there are a lot of scores of 15, my quartiles look like this:
- 1st: 1 to 14
- 2nd: 15 to 15
- 3rd: 15 to 15
- 4th: 16 to 20
So which quartile does a score of exactly 15 fall into?
As it falls into both the second and third quartiles, which quartile should be selected? For example - if this were used to rank a student's score, where should they fall?
Are there multiple ways of resolving this tie and if so, are there any that are statistically 'fairer'? Or is fairness an irrelevant concept here?