Question

Find out Quartile Deviation and Coefficient of Quartile Deviation of the following items:

145	130	200	210	198
234	159	160	178	257
260	300	345	360	390

Answer 1

S. No.	Item
1	130
2	145
3	159
4	160
5	178
6	198
7 8 9 10 11 12 13 14 15	200 210 234 257 260 300 345 360 390

We first arrange the given data in ascending order as above.

$$\begin{gathered} Q_1=\mathrm{Size}\mathrm{of}{\left(\frac{N+1}{4}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{\left(\frac{15+1}{4}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{4}^{\mathrm{th}}\mathrm{item}=160 \\ {Q}_{\mathit{3}}=\mathrm{Size}\mathrm{of}3{\left(\frac{N+1}{4}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{12}^{\mathrm{th}}\mathrm{item} \\ =300 \\ \mathrm{Quartile}\mathrm{Deviation}=\frac{Q_3-Q_1}{2}=\frac{300-160}{2} \\ =\frac{140}{2}=70 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{Q}.\mathrm{D}.=\frac{Q_3-Q_1}{Q_3+Q_1}=\frac{300-160}{300+160} \\ =\frac{140}{460}=0.304 \end{gathered}$$
Thus, the quartile deviation and coefficient of quartile deviation are 70 and 0.304 respectively.