Q$\mathrm{.}8.$ Polystyrene is a polymer material with the following repeat unit structure:

$[4]$

Calcualte the weight average molecular weight for polystyrene from the molecular weight data given below.

$\backslash$table$[[\backslash$table$[[$Molecular$],[$Weight Range$],[($g$/$mol$)]],\backslash$table$[[$x$\_(1)],[$number$],[$fraction$]],\backslash$table$[[$W $\_($i $)],[$weight fraction$]]],[12000-24000,0\mathrm{.}04,0\mathrm{.}04],[24000-36000,0\mathrm{.}11,0\mathrm{.}14],[36000-48000,0\mathrm{.}22,0\mathrm{.}24],[48000-60000,0\mathrm{.}27,0\mathrm{.}23],[60000-72000,0\mathrm{.}17,0\mathrm{.}16],[72000-84000,0\mathrm{.}11,0\mathrm{.}12],[84000-96000,0\mathrm{.}08,0\mathrm{.}07]]$