Quantiles of given data.

Question

Consider the data set $S = \{1,\,1,\,1,\,1,\,2,\,2,\,2,\,3,\,3,\,3,\,3,\,6,\,9\}$ to find the quartiles of this we have $$q_{1} = [0.25(13-1)]\text{th number} = 1.$$ $$q_{2} = [0.50(13-1)]\text{th number} = 2.$$ $$q_{3} = [0.75(13-1)]\text{th number} = 3.$$ Now if we have the set $S = \{1,\,1,\,1,\,1,\,2,\,2,\,2,\,3,\,3,\,3,\,3,\,6,\,9,\,12\}$ the quartiles are $$q_{1}=[0.25(14-1)]\text{th number} = 1.$$ $$q_{2}=[0.50(14-1)]\text{th number} = 2.$$ $$q_{3} = [0.75(14-1)]\text{th number} = 3.$$ Are these correct?

Answer 1

Yes your calculation is correct, but keep in mind, that if your caluclation says you should e.g. take the 2.5th number of $\{1,2,3,4\}$, sometimes people use the average of the two neighbouring numbers, in this case $0.5(2 + 3)$.