Mathematics - Statistics Question with Solution | TestHub

Since $0<y<x<2y$ $$\begin{array}{rl}& \therefore y>\frac{x}{2}\Rightarrow x-y<\frac{x}{2}\\ & \therefore x-y<y<x<2x+y\end{array}$$ Hence median $=\frac{y+x}{2}=10$ $\Rightarrow x+y=20$ And range $=(2x+y)-(x-y)=x+2y$ But range $=28$ $$\therefore x+2y=28$$ From equations (i) and (ii), $$\begin{array}{rl}& x=12,y=8\\ & \therefore \text{ Mean }\\ & =\frac{(x-y)+y+x+(2x+y)}{4}=\frac{4x+y}{4}\end{array}$$ $$=x+\frac{y}{4}=12+\frac{8}{4}=14$$