Question

Calculate coefficient of variation from the following data:

Marks (more than)	0	10	20	30	40	50	60	70
No. of students	100	90	75	50	20	10	5	0

Answer 1

Converting more than cumulative frequency distribution into simple frequency distribution:

Marks (X)	No. of Students (f)	Mid-Values (m)	fm	m2	fm2
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 −70 70 −80	100-90=10 90-75=15 75-50=25 50-20=30 20-10=10 10-5=5 5-0=5 0-0=0	5 15 25 35 45 55 65 75	50 225 625 1050 450 275 325 0	25 225 625 1225 2025 3025 4225 5625	250 3375 15625 36750 20250 15125 21125 0
	Σf =100		Σfm = 3000		Σfm2 =112500

$$\begin{gathered} Mean,\overline{X}=\frac{\Sigma fm}{\Sigma f}=\frac{3000}{100}=30 \\ \mathrm{Standard}\mathrm{deviation},\left(\sigma \right)=\sqrt{\frac{\Sigma f{m}^2}{\Sigma f}-{\left(\overline{X}\right)}^2} \\ =\sqrt{\frac{112500}{100}-{\left(30\right)}^2} \\ =\sqrt{1125-900} \\ =\sqrt{225}=15 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{variation}=\frac{\sigma }{\overline{X}}\times 100 \\ =\frac{15}{30}\times 100 \\ =50\% \end{gathered}$$