JEE Main 2024 — Statistics Question with Solution

\begin{aligned} & \mathrm{x}+\mathrm{y}=10 \ldots \ldots \ldots .(1) \\ & \text {Median }=18=\mathrm{M} \\ & \text {M.D. }=\frac{\sum \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|}{\sum \mathrm{f}_{\mathrm{i}}} \\ & 1.25=\frac{36+\mathrm{x}+2 \mathrm{y}}{40} \\ & \mathrm{x}+2 \mathrm{y}=14 \ldots \ldots \ldots .(2) \\ & \text { by (1) & (2) } \\ & \mathrm{x}=6, \mathrm{y}=4 \\ & \Rightarrow 4 \mathrm{x}+5 \mathrm{y}=24+20=44\end{aligned} $\begin{array}{|l|l|l|l|} \hline \operatorname{Age}\left(\mathrm{x}_{\mathrm{i}}\right) & \mathrm{f} & \left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right| & \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right| \\ \hline 15 & 5 & 3 & 15 \\ \hline 16 & 8 & 2 & 16 \\ \hline 17 & 5 & 1 & 5 \\ \hline 18 & 12 & 0 & 0 \\ \hline 19 & \mathrm{x} & 1 & \mathrm{x} \\ \hline 20 & \mathrm{y} & 2 & 2 \mathrm{y} \\ \hline \end{array}$