The median of the following observations arranged in ascending order is 64. Find the value of x :

No. of observations = 10, which is even.

Median = $\frac{\left(\frac{n}{2}\right)^\text{th}\text{term} + \left(\frac{n}{2} + 1\right)^\text{th}\text{term}}{2}$

$\left(\frac{n}{2}\right)^\text{th}\text{term} = \frac{10}{2}$ = 5^th term = x

$\left(\frac{n}{2} + 1\right)^\text{th}\text{term} = \frac{10}{2} + 1$ = 5 + 1 = 6^th term = x + 4

Given,

Median = 64

$$\begin{aligned}\therefore \frac{x + x + 4}{2} = 64 \\[1em] \Rightarrow \frac{2x + 4}{2} = 64 \\[1em] \Rightarrow \frac{2(x + 2)}{2} = 64 \\[1em] \Rightarrow x + 2 = 64 \\[1em] \Rightarrow x = 64 - 2 \\[1em] \Rightarrow x = 62\end{aligned}$$

Hence, Option 3 is the correct option.