Question

What are quartiles, deciles, and percentiles? State the general equation of computing the
ith quartile, jth decile, and kth percentile

Answer 1

The values that divide a list of numbers into quarters is a quartile.
A method of splitting up a set of ranked data into 10 equally large subsections is called deciles This type of data ranking is performed as part of many academic and statistical studies in the finance field. The data may be ranked from largest to smallest values, or vice versa.

Answer 2

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.

       15% percentile value means there are 15% of data items below this value.

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.

       A quartile means there are 25% of the given data items less than this quartile value.


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.

       A  decile value means that there are 10% of the data items given, below this value.