Question

Calculate Mean and Standard Deviation from the following data:

Marks ( Above)	:	0	10	20	30	40	50	60	70
No. of Students	:	100	90	75	50	25	15	5	0

Answer 1

As we are given marks (above) series, we can convert it into classes and frame the following table.

Marks	Mid Value (m)	cf	Frequency (f)	fm	Deviation from mean $$\begin{gathered} x=\left(m\mathit{-}\overline{X}\right) \\ \overline{X}=31 \end{gathered}$$	x2	fx2
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80	5 15 25 35 45 55 65 75	100 90 75 50 25 15 5 0	10 15 25 25 10 10 5 0	50 225 625 875 450 550 325 0	-26 -16 -6 4 14 24 34 44	676 256 36 16 196 576 1156 1936	6760 3840 900 400 1960 5760 5780 0
			Σf = 100	Σfm = 3100			Σfx2=25400

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }fm}{\mathrm{\Sigma }f}=\frac{3100}{100}=31 \\ SD=\sqrt{\frac{\mathrm{\Sigma }f{x}^2}{\mathrm{\Sigma }f}}=\sqrt{\frac{25400}{100}} \\ =\sqrt{254} \\ =15.93 \end{gathered}$$