The median of observations (written in ascending order) 26, 29, 42, 53, x, x + 2, 70, 75, 82, 83 and 100 is 65; then:

1. x = 65

2. x + 2 = 65

3. $\dfrac{x + (x + 2)}{2}$ = 6

4. none of these

Number of observations, n = 11 (odd)

By formula,

Median = $\Big[\dfrac{n + 1}{2}\Big]^{th}$ term

$\Rightarrow 65 = \Big[\dfrac{11 + 1}{2}\Big]^{th} \text{ term}\\[1em] \Rightarrow 65 = \Big[\dfrac{12}{2}\Big]^{th} \text{ term}\\[1em] \Rightarrow 65 = 6^{th} \text{ term}\\[1em] \Rightarrow 65 = x + 2.$

Hence, option 2 is the correct option.