Question

Find out Quartile Deviation , Coefficient of Quartile Deviation of the following data:

X	:	10	15	20	25	30	35	40	45
f	:	6	17	29	38	25	14	9	1

Answer 1

X	f	Cumulative Frequency
10	6	6
15	17	23
20	29	52
25	38	90
30	25	115
35	14	129
40	9	138
45	1	139
		N = 139

$$\begin{gathered} Q_1=\mathrm{Size}\mathrm{of}{\left(\frac{N+1}{4}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{\left(\frac{139+1}{4}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{35}^{\mathrm{th}}\mathrm{item} \end{gathered}$$
The 35^th item corresponds to 52 in the cumulative frequency.
$\therefore Q_1=20$

$$\begin{gathered} Q_{\mathit{3}}=\mathrm{Size}\mathrm{of}3{\left(\frac{N+1}{4}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{105}^{\mathrm{th}}\mathrm{item} \\ =30 \end{gathered}$$
The 105^th item corresponds to 115 in the cumulative frequency.
$\therefore Q_3=30$
$\mathrm{Coefficient}\mathrm{of}\mathrm{Q}.\mathrm{D}.=\frac{Q_3-Q_1}{Q_3+Q_1}=\frac{30-20}{30+20}=\frac{10}{50}=0.2$
Thus, coefficient of quartile deviation is 0.2.