code class$=$"asciimath"$>$Explain under what circumstances $\backslash$sum$\_($i$=1)^($i$=$I$)($P$\_($i$)*$R$\_($i$))/($T$\_($i$))$ is less than, equal to$,$ or greater than $\frac{{\displaystyle \underset{i=1}{\overset{i=\text{I}}{}}}{P}_i*{\displaystyle \underset{i=1}{\overset{i=\text{I}}{}}}{R}_i}{{\displaystyle \underset{i=1}{\overset{i=\text{I}}{}}}{T}_i}.$ I $am$ specifically interested $in$ argumentts regarding the ratio $of$ the median $to$ the mean for $P,R,$and $T.$ Write a proof $to$ show that your conclusion $is$ always true.