Question

Following are the marks obtained by 20 students in statistics. Find out coefficient of variation of the marks.

62	85	73	81	74	58	66	72	54	84
65	50	83	62	85	52	80	86	71	75

Answer 1

S. No.	Marks (X)	Deviation from mean $\left(\mathit{x}\mathbf{=}\mathit{X}\mathbf{-}\overline{\mathbf{X}}\right)$	Square deviation x2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20	62 85 73 81 74 58 66 72 54 84 65 50 83 62 85 52 80 86 71 75	−8.9 +14.1 +2.1 10.1 3.1 −12.9 −4.9 1.1 −16.9 13.1 −5.9 −20.9 12.1 −8.9 14.1 −18.9 9.1 15.1 .1 4.1	79.21 198.81 4.41 102.01 9.61 166.41 24.01 1.21 285.61 171.61 34.81 436.81 146.81 79.21 198.81 357.21 82.81 228.01 .01 16.81
	ΣX = 1418		Σx2 = 2623.8

$$\begin{gathered} \mathrm{Mean}\left(\overline{X}\right)=\frac{\mathrm{\Sigma }X}{N}=\frac{1418}{20}=70.9 \\ \mathrm{Standard}\mathrm{deviation}\left(\mathrm{\sigma }\right)=\sqrt{\frac{x^2}{N}} \\ \mathrm{or},\sigma =\sqrt{\frac{2623.8}{20}} \\ \mathrm{or},\sigma =\sqrt{131.19} \\ \Rightarrow \sigma =11.45 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{variation}\left(\mathrm{CV}\right)=\frac{\mathrm{\sigma }}{\overline{X}}\times 100 \\ \mathrm{or},\mathrm{CV}=\frac{11.45}{70.9}\times 100 \\ \Rightarrow \mathrm{CV}=16.14 \end{gathered}$$

Hence, coefficient of variation (CV) of the marks is 16.14