A refinement over the usual formulae for deciles

The formulae for the median (fifth decile) is well defined in the literature. But the formulae for other deciles available in the literature are conflicting in the sense that they do not divide the ordered sample observations into ten segments having the same number of observations in each. It is observed that the ranks of a particular decile for any two sample sizes with a fixed remainder, with respect to modulus10, differs by an integer. The remainder is also observed to be the number of deciles having integer ranks. Prompted by these ideas, the remainder and the usual linear interpolation are exploited to find deciles.