Question

Find out quartile deviation and the coefficient of quartile deviation of the following series.
Wages of 9 workers in Rupees:
170, 82, 110, 100, 150, 150, 200, 116, 250

Answer 1

Arranging the data in the ascending order as presented below.
82, 100, 110, 116, 150, 150, 170, 200, 250
Here, N = 9
$$\begin{gathered} Q_1=\mathrm{size}\mathrm{of}{\left(\frac{9+1}{4}\right)}^{th}=\mathrm{size}\mathrm{of}2.5^{\mathrm{th}}\mathrm{item} \\ =\mathrm{size}\mathrm{of}{2}^{nd}\mathrm{item}+0.5\left(\mathrm{size}\mathrm{of}{3}^{rd}\mathrm{item}-\mathrm{size}\mathrm{of}{2}^{nd}\mathrm{item}\right) \\ =100+0.5\left(110-100\right)=105 \\ {\mathrm{Q}}_3=\mathrm{size}\mathrm{of}3{\left(\frac{9+1}{4}\right)}^{th}\mathrm{item}=\mathrm{size}\mathrm{of}7.5^{\mathrm{th}}\mathrm{item} \\ =\mathrm{size}\mathrm{of}{7}^{th}\mathrm{item}+0.5\left(\mathrm{size}\mathrm{of}{8}^{\mathit{t}\mathit{h}}\mathrm{item}-\mathrm{size}\mathrm{of}{7}^{\mathrm{th}}\mathrm{item}\right) \\ =170+0.5\left(200-170\right)=185 \\ Q\mathit{.}D\mathit{.}=\frac{{\mathit{Q}}_{\mathit{3}}\mathit{-}{\mathit{Q}}_{\mathit{1}}}{\mathit{2}}=\frac{185-105}{2}=40 \end{gathered}$$

$\mathrm{Coefficient}\mathrm{of}\mathrm{Q}.\mathrm{D}.=\frac{Q_3-Q_1}{Q_3+Q_1}=\frac{185-105}{185+105}=0.276$