Consider the following distribution 30, 34, 35, 36, 37, 38, 39, 40. If the value 35 is removed from the given data, then the median changes by :

Given,

The distribution is 30, 34, 35, 36, 37, 38, 39, 40.

The data is already arranged in ascending order.

Here, $n = 8$, which is even.

By formula,

$$\begin{aligned}\text{Median} = \frac{1}{2}\Big[\Big(\frac{n}{2}\Big)^{th} \text{term} + \Big(\frac{n}{2} + 1\Big)^{th} \text{term}\Big] \\[1em] = \frac{1}{2}[4^{th} \text{ term} + 5^{th} \text{ term}] \\[1em] = \frac{36 + 37}{2} \\[1em] = \frac{73}{2} \\[1em] = 36.5\end{aligned}$$

On removing the value 35, the distribution becomes 30, 34, 36, 37, 38, 39, 40.

Here, $n = 7$, which is odd.

By formula,

$$\begin{aligned}\text{Median} = \Big(\frac{n + 1}{2}\Big)^{th} \text{ term} \\[1em] = 4^{th} \text{ term} \\[1em] = 37\end{aligned}$$

Change in median = 37 − 36.5 = 0.5.

Hence, option 1 is the correct option.