Measures of Dispersion — Maths STD 11 Science — Question

Calculation of variance of u:

$\overline{ u }=\frac{\sum f _{ i } u _{ i }}{ N }=\frac{-32}{70}=-0.4571$

$\operatorname{Var}( u )=\sigma_{ u }{ }^2=\frac{\sum f _{ i } u _{ i }{ }^2}{ N }-(\overline{ u })^2=\frac{296}{70}-(-0.4571)^2$

$\begin{aligned} & =4.2286-0.2089 \\ & =4.0197\end{aligned}$

$\begin{aligned} & \operatorname{Var}( X )= h ^2 \operatorname{Var}( u )=(1)^2 \times 4.0197=4.0197 \\ & \text { S.D. }=\sigma_x=\sqrt{\operatorname{Var}( X )}=\sqrt{4.0197}=2.005\end{aligned}$