Question

Calculate interquartile range, quartile deviation and coefficient of quartile deviation from the following data:

Family	A	B	C	D	E	F	G
Income (in ₹)	1,200	1,400	1,500	1,700	2,000	2,100	2,200

Answer 1

Family	S. No.	Income Rs
A	1	1200
B	2	1400
C	3	1500
D	4	1700
E	5	2000
F	6	2100
G	7	2200
	N = 7

$$\begin{gathered} Q_1=\mathrm{Size}\mathrm{of}{\left[\frac{N+1}{4}\right]}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{\left[\frac{7+1}{4}\right]}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{2}^{\mathrm{nd}}\mathrm{item}=1400 \\ {Q}_3=\mathrm{Size}\mathrm{of}3{\left[\frac{N+1}{4}\right]}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}3{\left[\frac{7+1}{4}\right]}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{6}^{\mathrm{th}}\mathrm{item}=2100 \\ \mathit{I}\mathit{n}\mathit{t}\mathit{e}\mathit{r}\mathbf{}\mathit{Q}\mathit{u}\mathit{a}\mathit{r}\mathit{t}\mathit{i}\mathit{l}\mathit{e}\mathbf{}\mathit{R}\mathit{a}\mathit{n}\mathit{g}\mathit{e}=Q_3-Q_1=2100-1400=700 \\ \mathit{Q}\mathit{u}\mathit{a}\mathit{r}\mathit{t}\mathit{i}\mathit{l}\mathit{e}\mathbf{}\mathit{d}\mathit{e}\mathit{v}\mathit{i}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}=\frac{Q_3-Q_1}{2}=\frac{700}{2}=350 \end{gathered}$$

$\mathit{C}\mathit{o}\mathit{e}\mathit{f}\mathit{f}\mathit{i}\mathit{c}\mathit{i}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{Q}\mathbf{.}\mathit{D}\mathbf{.}=\frac{Q_3-Q_1}{Q_3+Q_1}=\frac{2100-1400}{2100+1400}=\frac{700}{3500}=0.2$