Question

Calculate arithmetic mean, standard deviation and variance from the following series:

Marks	:	70-80	60-70	50-60	40-50	30-40	20-30
No of students	:	7	11	22	0	15	5

Answer 1

Marks	Mid Value (m)	f	fm	Deviation from mean $$\begin{gathered} x=\left(m-\overline{\mathit{X}}\right) \\ \overline{\mathit{X}}=51.67 \end{gathered}$$	x2	fx2
20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80	25 35 45 55 65 75	5 15 0 22 11 7	125 525 0 1210 715 525	26.67 16.67 6.67 3.33 13.33 23.33	711.29 277.89 44.49 11.09 177.69 544.29	3556.45 4168.35 0 243.98 1954.59 3810.03
		Σf = 60	Σfm = 3100			Σfx2 = 13733.4

$$\begin{gathered} \overline{\mathit{X}}=\frac{\mathrm{\Sigma }fm}{\mathrm{\Sigma }f}=\frac{3100}{60}=51.67 \\ SD=\sqrt{\frac{\mathrm{\Sigma }f{x}^2}{\mathrm{N}}}=\sqrt{\frac{13733.4}{60}}=\sqrt{228.89}=15.13 \\ \mathrm{Variance}={\left(SD\right)}^2=228.89 \end{gathered}$$