Question

Given the following data, calculate coefficient of variation:

Age	20−30	30−40	40−50	50−60	60−70	70−80	80−90
Number of Students	3	61	132	153	140	51	2

Answer 1

Age	Mid Value (m)	Frequency (f)	Deviation from Assumed mean (dx = X − A) (A = 55)	$d_x\text{'}=\frac{d_x}{i}=\frac{d_x}{10}$	$f\times d_x\text{'}=f{d}_x\text{'}$	$f\times d_x{\text{'}}^2=f{d}_x{\text{'}}^2$
20−30 30 −40 40 −50 50 −60 60 −70 70 −80 80 −90	25 35 45 $\boxed{55=\mathrm{A}}$ 65 75 85	3 61 132 153 140 51 2	−30 −20 −10 0 10 20 30	−3 −2 −1 0 1 2 3	−9 −122 −132 0 140 102 6	27 244 132 0 140 204 18
		N = 542			Σfdx'= -15	Σfdx'2 =765

$$\begin{gathered} \mathrm{Mean}\left(\overline{X}\right)=\mathrm{A}+\frac{\mathrm{\Sigma }f{d}_x\text{'}}{N}\times i \\ or,\overline{X}=55+\frac{\left(-15\right)}{542}\times 10 \\ or,\overline{X}=55-.28 \\ \Rightarrow \overline{X}=54.72 \\ \mathrm{Standard}\mathrm{Deviation}\left(\mathrm{\sigma }\right)=\sqrt{\frac{\mathrm{\Sigma }f{d}_x{\text{'}}^2}{N}-{\left(\frac{\mathrm{\Sigma }f{d}_x\text{'}}{N}\right)}^2}\times i \\ or,\mathrm{\sigma }=\sqrt{\frac{765}{542}-{\left(\frac{-15}{542}\right)}^2}\times 10 \\ or,\mathrm{\sigma }=\sqrt{1.41-{\left(-0.03\right)}^2}\times 10 \\ or,\mathrm{\sigma }=\sqrt{1.41-0.0009}\times 10 \\ or,\mathrm{\sigma }=1.187\times 10 \\ \Rightarrow \mathrm{\sigma }=11.87 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{Variation}\left(CV\right)=\frac{\mathrm{\sigma }}{\overline{X}}\times 100 \\ or,CV=\frac{11.87}{54.72}\times 100 \\ or,CV=\frac{1190}{54.72} \\ \Rightarrow CV=21.69 \end{gathered}$$

Hence, Coefficient of variation is 21.69