JEE Main 2026 — 28 January, Morning Shift — Question 14

$$\frac{2+3+5+10+11+13+15+21+a+b}{10}=9$$ $$\begin{gathered} \frac{80+a+b}{10}=9 \Rightarrow a+b=10 \end{gathered}$$ $$\frac{\Sigma x_i^2}{10} - \left( \frac{\Sigma x_i}{10} \right)^2 = 34.2$$

$\frac{2^2+3^2+5^2+10^2+11^2+13^2+15^2+21^2+a^2+b^2}{10} - 9^2 = 34.2$ $1094 + a^2 + b^2 - 810 = 342$ $\begin{gathered} a^2 + b^2 = 58 \end{gathered}$ $a=7,\ b=3$ or $a=3,\ b=7$

Number: 2, 3, 5, 7, 10, 11, 13, 15, 21 Mean $=\frac{7+10}{2}=8.5$

$$\mathrm{M.D.} = \frac{6.5+5.5+5.5+3.5+1.5+1.5+2.5+4.5+6.5+12.5}{10} = \frac{50}{5} = 5$$