Q. The quartile deviation for the following data is [table] $\mathbf{x}$ | 2 | 3 | 4 | 5 | 6 ; $\mathbf{f}$ | 3 | 4 | 8 | 4 | 1 [/table]
A) 0
B) $\frac{1}{4}$
C) $\frac{1}{2}$
D) 1
Explanation
(d)
Here, $N = \Sigma f = 20$
Q$\ _{1} = \frac{N + 1}{4}th = \left( \frac{21}{4} \right)th = 3rd\$observation
Similarly, $Q_{3} = 3\left( \frac{N + 1}{4} \right)th$
=$\left( \frac{63}{4} \right)th = 5\ th$ observation
$\therefore\$ QD$= \frac{1}{2}\left( Q_{3} - Q_{1} \right) = \frac{1}{2}(5 - 3) = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.