Question

Calculate Quartile Deviation and its Coefficient of Rajesh's daily income.

Months	:	1	2	3	4	5	6	7	8	9	10	11
Income (₹)	:	239	250	251	251	257	258	260	261	262	262	273

Answer 1

Month	Income (Rs)	Month	Income (Rs)
1	239	7	260
2	250	8	261
3	251	9	262
4	251	10	262
5	257	11	273
6	258

N = 11
$$\begin{gathered} Q_1=\mathrm{Size}\mathrm{of}{\left(\frac{N+1}{4}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{\left(\frac{11+1}{4}\right)}^{\mathrm{th}}\mathrm{item}=3^{rd}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{3}^{\mathrm{rd}}\mathrm{item} \\ =251 \\ {Q}_{\mathit{3}}=\mathrm{Size}\mathrm{of}3{\left(\frac{N+1}{4}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}3{\left(3\right)}^{rd}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{9}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{9}^{\mathrm{th}}\mathrm{item} \\ =262 \\ \mathrm{Quartile}\mathrm{deviation}=\frac{Q_3-Q_1}{2} \\ =\frac{262-251}{2} \\ =\frac{11}{2}=5.5 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{Q}.\mathrm{D}.=\frac{Q_3-Q_1}{Q_3+Q_1} \\ =\frac{262-251}{262+251} \\ =\frac{11}{513}=0.0214 \end{gathered}$$
Thus, the quartile deviation and coefficient of quartile deviation are 5.5 and 0.021 respectively.