Measures of Dispersion — Maths STD 11 Science — Question

let $u=\frac{x-A}{ h }=\frac{x-54.5}{10}$

Calculation of variance of u:

$\overline{ u }=\frac{\sum f _{ i } u _{ i }}{ N }=\frac{-293}{400}=-0.7325$

$\operatorname{Var}(u)=\sigma_u{ }^2=\frac{\sum f_i u_i{ }^2}{N}-(\bar{u})^2$

$=\frac{1351}{400}-(-0.7325)^2$

$=3.3775-0.5366=2.8409$

$\begin{aligned} \therefore \quad \operatorname{Var}( X )= h ^2 \operatorname{var}( u ) & =(10)^2 \times 2.8409 \\ & =100 \times 2.8409\end{aligned}$

$=284.09$

$\therefore \quad$ S.D. $=\sigma_x=\sqrt{\operatorname{Var}(X)}=\sqrt{284.09}=16.85$