Question

Find the Quartile Deviation and its Coefficient from the following data relating to the daily wages of seven workers:

Daily Wages ( in ₹)

:

50

90

70

40

80

65

60

Answer 1

S. No.	Daily Wages
1	40
2	50
3	60
4	65
5	70
6	80
7	90

For the calculation of quartile deviation, we first arrange the given data in ascending order as above. The quartile deviation is then calculated in the following manner.
$$\begin{gathered} Q_1=\mathrm{Size}\mathrm{of}{\left(\frac{N+1}{4}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{\left(\frac{7+1}{4}\right)}^{\mathrm{th}}\mathrm{item}=\mathrm{Size}\mathrm{of}{2}^{\mathrm{nd}}\mathrm{item} \\ =50 \\ {Q}_{\mathit{3}}=\mathrm{Size}\mathrm{of}3{\left(\frac{N+1}{4}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{6}^{\mathrm{th}}\mathrm{item}=80 \\ \mathrm{Quartile}\mathrm{deviation}=\frac{Q_3-Q_1}{2}=\frac{80-50}{2}=\frac{30}{2}=15 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{Q}.\mathrm{D}.=\frac{Q_3-Q_1}{Q_3+Q_1} \\ =\frac{80-50}{80+50}=\frac{30}{130}=0.23 \end{gathered}$$
Thus, the quartile deviation and coefficient of quartile deviation are 15 and 0.23 respectively.