Solution
\[
\begin{aligned}
& \mathrm{k}, 2 \mathrm{k}, 3 \mathrm{k}, \ldots \ldots, 500 \mathrm{k}, 501 \mathrm{k}, \ldots, 1000 \mathrm{k} \\
& \text { Median }=\frac{500 \mathrm{k}+501 \mathrm{k}}{2}=1001 \frac{\mathrm{k}}{2}=\overline{\mathrm{x}} \\
& \text { Mean deviation about mean }=\frac{\sum_{\mathrm{i}=1}^{\mathrm{n}}\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|}{\mathrm{n}}=500 \\
& \Rightarrow \frac{\left[\frac{999|\mathrm{k}|}{2}+\frac{997|\mathrm{k}|}{2}+\cdots+\frac{|\mathrm{k}|}{2}+\frac{|\mathrm{k}|}{2}+\frac{3|\mathrm{k}|}{2}+\cdots+\frac{999|\mathrm{k}|}{2}\right]}{1000}=500 \\
& \Rightarrow|\mathrm{k}|+3|\mathrm{k}|+5|\mathrm{k}|+\cdots+997|\mathrm{k}|+999|\mathrm{k}|=500 \times 1000 \\
& \Rightarrow \frac{500}{2}[|\mathrm{k}|+999|\mathrm{k}|]=500 \times 1000 \\
& \Rightarrow 1000|\mathrm{k}|=2 \times 1000 \Rightarrow|\mathrm{k}|=2 \\
& \mathrm{k}^{2}=|\mathrm{k}|^{2}=4 \text { Answer }(2)
\end{aligned}
\]
.
