The median of the data

78, 56, 22, 34, 45, 54, 39, 68, 54, 84 is

1. 45

2. 49.5

3. 54

4. 56

Arranging given data in ascending order :

22, 34, 39, 45, 54, 54, 56, 68, 78, 84.

No. of observation (n) = 10.

Here, n is even.

By formula,

$\text{Median} = \dfrac{\dfrac{n}{2} \text{th observation} + \Big(\dfrac{n}{2} + 1\Big) \text{th observation}}{2} \\[1em] = \dfrac{\dfrac{10}{2} \text{th observation} + \Big(\dfrac{10}{2} + 1\Big) \text{th observation}}{2} \\[1em] = \dfrac{\text{5th observation + 6th observation}}{2} \\[1em] = \dfrac{54 + 54}{2} \\[1em] = \dfrac{108}{2} \\[1em] = 54.$

Hence, Option 3 is the correct option.