Question

Calculate standard deviation of marks secured by 100 examinees in the examination:

Marks	10−20	20−30	30−40	40−50	50−60	60−70	70−80	80−90
Number of Examinees	19	3	2	49	24	2	0	1

Answer 1

X	Mid Values m	f	fX	$x\mathit{=}X\mathit{-}\mathit{}\overline{\mathit{X}}$	x2	fx2
10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80 80 − 90	15 25 35 45 55 65 75 85	19 3 2 49 24 2 0 1	285 75 70 2205 1320 130 0 85	−26.70 −16.70 −6.7 3.3 13.3 23.3 33.3 43.3	712.89 278.89 44.89 10.89 176.89 542.89 1108.89 1874.89	13544.91 836.67 89.78 533.61 4245.36 1085.78 0 1874.89
		∑f = 100	∑fX = 4170			∑fx2 = 22211

$$\begin{gathered} \overline{X}=\frac{{\sum }_{}^{}fX}{{\sum }_{}^{}f}=\frac{4170}{100}=41.70 \\ \mathrm{Standard}\mathrm{Deviation}\left(\sigma \right)=\sqrt{\frac{{\sum }_{}^{}f{x}^2}{{\sum }_{}^{}f}}=\sqrt{\frac{22211}{100}}=14.90 \end{gathered}$$