Explain under what circumstances $\backslash$sum$\_($i$=1)^($i$=$I$)($P$\_($i$)*$R$\_($i$))/($T$\_($i$))$ is less than, equal to$,$ or greater than $(\backslash$sum$\_($i$=1)^($i$=$I$)$ P$\_($i$)*\backslash$sum$\_($i$=1)^($i$=$I$)$ R$\_($i$))/(\backslash$sum$\_($i$=1)^($i$=$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.