JEE Main 2026 — 23 January, Morning Shift — Question 13

Mean $=\frac{-18+\mathrm{x}+\mathrm{y}+2+9+16}{8}=\frac{7}{3}$

$\begin{gathered} =\frac{x+y+9}{8}=\frac{7}{2} \Rightarrow x+y+9=28 \end{gathered}$ Variance $=\frac{\sum \mathrm{z}_{\mathrm{i}}^{2}}{8}-(\mu)^{2}=\frac{293}{4}$ $\begin{gathered} \Rightarrow \frac{10^{2}+7^{2}+1^{2}+\mathrm{x}^{2}+\mathrm{y}^{2}+2^{2}+9^{2}+16^{2}}{8}-\left(\frac{7}{2}\right)^{2}=\frac{293}{4} \end{gathered}$ Solving & $\Rightarrow \mathrm{x}=12, \mathrm{y}=7$

Mean of $(1+x+y), x, y,|y-x|$ is $\Rightarrow \frac{20+12+7+5}{4}=\frac{44}{4}=11$