How to Locate a Quantile

HOW TO LOCATE A QUANTILE

Below is a universal procedure for locating any quantile (Qi). It is my original method.

o = (i(n))/T

o = quantile location

i = subscript of ith quantile

n = no. of observations

T = total no. of parts

Is o a whole number?

If Yes then Qi = (Xo + Xo+1)/2

If No then Qi = Xc(o+1)

Qi = ith quantile

Xo = oth observation

Xo+1 = o+1th observation

c(o) = whole (cardinal) number part of o

Xc(o) = observation corresponding to whole (cardinal) number part of o

c(o+1) = whole (cardinal) number part of o+1

Xc(o+1) = observation corresponding to whole (cardinal) number part of o+1

ILLUSTRATION

Let’s suppose you want to locate the seventh nonile or Q7 in an ordered array of 121 numbers.

i = 7

n = 121

T = 9

o = (7*121)/9 = 94.11

Is o a whole number? No.

c(o+1) = c(94.11+1) = 95

Qi = Q7 = Xc(o+1) = X95

The seventh nonile or Q7 in the ordered array is the 95th number in the array, or X95.