If 25 is removed from the data 20, 24, 25, 26, 27, 28, 29, 30, then the median increases by:

1. 0.5

2. 1

3. 1.5

4. 2

Set of observations = 20, 24, 25, 26, 27, 28, 29, 30

Here, n = 8, which is even.

By formula,

Median = $\dfrac{\dfrac{\text{n}}{2} \text{ th observation} + \Big(\dfrac{\text{n}}{2} + 1\Big) \text{ th observation}}{2}$

$= \dfrac{\dfrac{8}{2} \text{ th observation} + \Big(\dfrac{8}{2} + 1\Big) \text{ th observation}}{2} \\[1em] = \dfrac{4 \text{ th observation} + \Big(4 + 1\Big) \text{ th observation}}{2} \\[1em] = \dfrac{4 \text{ th observation} + 5 \text{ th observation}}{2} \\[1em] = \dfrac{26 + 27}{2} \\[1em] = \dfrac{53}{2} \\[1em] = 26.5$

If 25 is removed from given set, then we get:

Set of observations = 20, 24, 26, 27, 28, 29, 30

Here, n = 7, which is odd.

By formula,

Median = $\dfrac{\text{n} + 1}{2} \text{ th observation}$

$= \dfrac{7 + 1}{2} \text{ th observation} \\[1em] = \dfrac{8}{2} \text{ th observation} \\[1em] = 4 \text{ th observation} \\[1em] = 27$

Difference between median = 27 - 26.5 = 0.5

Hence, Option 1 is the correct option.