Question

Quartile deviation of the following numbers $10,8,12,11,14,9,6$ is?

• A. $2$
• B. $10$
• C. $1/2$
• D. $1$

Answer 1

Answer: (A)

$2$

Arranging given numbers in ascending order,

$6,8,9,10,11,12,14$

Number of observation $\left(N\right)=7$

$Q_i={\left\{i\left(\frac{N+1}{4}\right)\right\}}^{th}term$

$Q_1={\left\{1.\left(\frac{7+1}{4}\right)\right\}}^{th}term=2^{nd}term$

$2^{nd}term=8$

$\therefore$ $Q_1=8$

$Q_3={\left\{3.\left(\frac{7+1}{4}\right)\right\}}^{th}term=6^{th}term$

$6^{th}term=12$

$\therefore$ $Q_3=12$

$\therefore$ Quartile deviation $=\frac{1}{2}(Q_3-Q_1)$

$=\frac{1}{2}(12-8)$

$=\frac{4}{2}$

$=2$