Question

Following are the marks of the students. Find mean deviation and coefficient mean deviation from mean.

Marks	5	10	15	20	25	30	35	40
No. of students	16	32	36	44	28	18	12	14

Answer 1

Marks (X)	Frequency (f)	fX	Deviation from Mean $$\begin{gathered} \left|d_{\overline{X}}\right|=\left|X-\overline{X}\right| \\ \left|X-20.2\right| \end{gathered}$$	$\mathit{f}\mathbf{\times }\left|{\mathbf{d}}_{\overline{\mathbf{X}}}\right|\mathbf{=}\mathit{f}\left|{\mathbf{d}}_{\overline{\mathbf{X}}}\right|$
5	16	80	15.2	243.2
10	32	320	10.2	326.4
15	36	540	5.2	187.2
20	44	880	0.2	8.8
25	28	700	4.8	134.4
30	18	540	9.8	176.4
35	12	420	14.8	177.6
40	14	560	19.8	277.2
ΣX = 180	Σf = 200	ΣfX=4040		Σ$f\left|d\overline{{}_X}\right|$=1531.2

$$\begin{gathered} \mathrm{Mean}\left(\overline{X}\right)=\frac{\Sigma fX}{\Sigma f}=\frac{4040}{200}=20.2 \\ \mathrm{Thus},\mathrm{calculate}\mathrm{the}\mathrm{deviation}\mathrm{of}\mathrm{the}\mathrm{values}\mathrm{from}20.2 \\ \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Mean}\left(M{D}_{\overline{X}}\right)=\frac{\Sigma f\left|d\overline{{}_X}\right|}{\Sigma f}=\frac{1531.2}{200}=7.65 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{Mean}\mathrm{deviation}=\frac{M{D}_{\overline{X}}}{\overline{X}}=\frac{7.65}{20.2}=0.379=0.38approx. \end{gathered}$$