$[4]$ When PP$,$ one of the representative polymers, was synthesized, it showed the following molecular weight distribution, and the degree of polymerization was analyzed as about $571.$ Answer the following question to obtain the weight$-$average molecular weight of this polymer. $[$Short answer type, $30$ points$]$

$\backslash$table$[[$Molecular weight range $($g$/$mol$),$Number fraction $(x_i)$