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Q$2)$ An initial charge of particle $($A$)$ of $450gm$ is mixed with $550gm$ of particle $($B$)$ in a reactor. After $1$ minute of mixing five spot samples, each containing an average number of particles about $60$ particles, for the evaluation of the performance of the mixture, calculate:

i$.$ the standard deviation

ii$.$ the mixing index $(I_s),$ and the least value of the mixing index $(I_{s,0}).$

iii. the mixing index after a time of $145$ seconds.

$\backslash$table$[[$Numper of fraction of B$,$Sample$],[0\mathrm{.}45,1],[0\mathrm{.}50,2],[0\mathrm{.}65,3],[0\mathrm{.}55,4],[0\mathrm{.}40,5]]$