Assertion (A) : If the median of the observations 11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38 and 47, arranged in ascending order is 24, then the value of x is 20.

Reason (R) : For an ungrouped data, containing n observations, the median is given by

Median = $\dfrac{\text{n}}{2}$ th observation, where n is odd.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

We know that,

For an ungrouped data, containing n observations, the median is given by

Median = $\dfrac{\text{n} + 1}{2}$ th observation, where n is odd.

∴ Reason (R) is false.

Arranging the given data in ascending order,

11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38, 47

Given, Median = 24

Here, n = 9, which is odd.

$\Rightarrow \text{Median} = \dfrac{\text{n} + 1}{2} \text{th observation} \\[1em] \Rightarrow 24 = \dfrac{9 + 1}{2} \text{th observation} \\[1em] \Rightarrow 24 = \dfrac{10}{2} \text{th observation} \\[1em] \Rightarrow 24 = 5 \text{th observation}$

⇒ 24 = x + 4

⇒ x = 24 - 4

⇒ x = 20.

∴ Assertion (A) is true.

Hence, Option 1 is the correct option.