Measures of Dispersion — Maths STD 11 Science — Question

Calculation of variance of u:

$\begin{aligned} & \overline{ u }=\frac{\sum f _i u _i}{ N }=\frac{-55}{110}=-0.5 \\ & \bar{x}=\overline{ u } \times h + A =(-0.5) \times 1000+6500=-500+6500=6000\end{aligned}$

$\begin{aligned} \operatorname{Var}( u )=\sigma_{ u }^2 & =\frac{\sum f _{ i } u _i^2}{ N }-(\overline{ u })^2=\frac{417}{110}-(-0.5)^2 \\ & =3.79-0.25\end{aligned}$

$=3.54$

$\begin{aligned} & \operatorname{Var}( X )= h ^2 \operatorname{Var}( u )=(1000)^2 \times 3.54=3540000 \\ & \text { S.D. }=\sigma_x=\sqrt{\operatorname{Var}( X )}=\sqrt{3540000}=1881.48 \\ & \text { C. V. }=100 \times \frac{\sigma_x}{\bar{x}}=100 \times \frac{1881.48}{6000}=31.36 \%\end{aligned}$