In a data, 10 numbers are arranged in ascending order. If the 8th entry is increased by 6, then the median increases by

1. 0

2. 2

3. 3

4. 6

Since, number of observations (n) = 10, which is even.

By formula,

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

Since, 5th and 6th observation is not changed at all, so there is no change in median.

Hence, Option 1 is the correct option.