Question

Compute coefficient of Quartile deviation form the following data:

Marks	10	20	30	40	50	60
No. of students	4	7	15	8	7	2

Answer 1

Marks	No. of Students	Cumulative Frequency
10	4	4
20	7	7 + 4 = 11
30	15	11 + 15 = 26
40	8	26 + 8 = 34
50	7	34 + 7 = 41
60	2	41 + 2 = 43
	N = 43

$$\begin{gathered} Q_1=\mathrm{Size}\mathrm{of}{\left[\frac{N+1}{4}\right]}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{\left[\frac{43+1}{4}\right]}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{11}^{\mathrm{th}}\mathrm{item} \\ Now,weneedtolocatethisiteminthecolumnofCumulativeFrequency.Thisitemiscorrespondingtovalue20 \\ Hence,Q_1=20 \\ Similarly, \\ {Q}_3=\mathrm{Size}\mathrm{of}3{\left[\frac{N+1}{4}\right]}^{\mathrm{th}}\mathrm{item} \\ =S\mathrm{ize}\mathrm{of}3{\left[\frac{43+1}{4}\right]}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{33}^{\mathrm{rd}}\mathrm{item}=40 \end{gathered}$$

$\mathit{C}\mathit{o}\mathit{e}\mathit{f}\mathit{f}\mathit{i}\mathit{c}\mathit{i}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{Q}\mathbf{.}\mathit{D}.=\frac{Q_3-Q_1}{Q_3+Q_1}=\frac{40-20}{40+20}=\frac{20}{60}=0.333$