Measures of Dispersion — Maths STD 11 Science — Question

Let $u =\frac{ x - A }{ h }=\frac{ x -74.5}{10}$

Calculation of variance of u:

$\begin{aligned} \overline{ u } & =\frac{\sum f _{ i } u _i}{ N }=\frac{-25}{100}=-0.25 \\ \bar{x} & =\overline{ u } \times h + A \\ & =-0.25 \times 10+74.5\end{aligned}$

$=72$

$\begin{aligned} \operatorname{Var}( u ) & =\sigma_{ u }{ }^2=\frac{\sum f _{ i } u _{ i }{ }^2}{ N }-(\overline{ u })^2 \\ & =\frac{155}{100}-(-0.25)^2 \\ & =1.55-0.0625 \\ & =1.4875\end{aligned}$

$\begin{aligned} & \therefore \operatorname{Var}(X)= h ^2 \operatorname{var}( U ) \\ & =(10)^2 \times 1.4875 \\ & =100 \times 1.4875 \\ & =148.75 \\ & \therefore \text { S.D. }=\sigma_{ X }=\sqrt{ } \operatorname{Var}( X ) \\ & =\sqrt{ } 148.75 \\ & =12.2\end{aligned}$