Question

The quartile deviation for the following data is

x :	2	3	4	5	6
f :	3	4	8	4	1

• A. 0
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. 1

Answer 1

Answer: (D)

1

Answer 2

$N = (\Sigma f) = 20$

$Q_{1} = \frac{(N + 1)}{4}th$ observation $= \left( \frac{21}{4} \right)^{th}$observation=3

Similarly, $Q_{3} = 3\left( \frac{N + 1}{4} \right)\mspace{6mu} th$ observation

$= \left( \frac{63}{4} \right)\mspace{6mu} th$ observation = 5

Now Q.D. $= \frac{1}{2}\left( Q_{3} - Q_{1} \right) = \frac{1}{2}\left( Q_{3} - Q_{1} \right) = \frac{1}{2}(5 - 3) = 1$.