Question

State the general equation of computing the i^th quartile, j^th decile and k^th percentile.

Answer 1

percentile:
         n = k / 100 * N,  
         n = (ordinal) rank of the data that corresponds to the k th percentile,  in a sequence or list of N data items.  The data items are arranged in increasing order.  After calculating n, find  the nth item in the data list.  If n is a fraction, then take the upper integer.

quartile
       quartile means 25 percentile.    i th quartile means  i * 25 percentile.
                  n = i * 25 /100 * N = i * N / 4

       After finding n, Find n th item in the ordered list of data items.  If n is a fraction, take the upper integer.

decile
         decile means 10 percentile.    j th decile means  i * 10 percentile.
                  n = j * 10 /100 * N = j * N / 10

       After finding n, Find n th item in the ordered list of data items.  If n is a fraction, take the upper integer.