Question

Calculate coefficient of variation of the following data:

S. No.	1	2	3	4	5	6	7	8
Value	25	42	33	48	45	29	43	39

Answer 1

S. No.	Value (X)	Deviation from mean $\left(x=X-\overline{X}\right)$	x2
1 2 3 4 5 6 7 8	25 42 33 48 45 29 43 39	−13 4 −5 10 7 −9 5 1	169 16 25 100 49 81 25 1
N = 8	ΣX = 304		Σx2 = 466

$$\begin{gathered} \mathrm{Mean}\left(\overline{X}\right)=\frac{\mathrm{\Sigma X}}{N}=\frac{304}{8}=38 \\ \mathrm{Standard}\mathrm{deviation}(\mathrm{\sigma })=\sqrt{\frac{\mathrm{\Sigma }{x}^2}{N}}=\sqrt{\frac{466}{8}}=\sqrt{58.25}=7.63 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{variation}\left(\mathrm{CV}\right)=\frac{\mathrm{\sigma }}{\overline{X}}\times 100=\frac{7.63}{38}\times 100=\frac{763}{38}=20.08 \end{gathered}$$

Hence, coefficient of variation is 20.08