Assertion (A) : The numbers 8, 10, 12, x and 15 are in ascending order of their values. If the mean of their observations is equal to their median, the value of x is 15.

Reason (R) : If the number of observations is n, their mean = $\dfrac{\text{Sum of observations}}{n}$ and median (if n is odd) = value of the $\Big(\dfrac{n + 1}{2}\Big)^{\text{th}}$ observation

1. A is true, R is true

2. A is true, R is false

3. A is false, R is true

4. A is false, R is false

Numbers : 8, 10, 12, x and 15.

n = 5, which is odd

Median = $\Big(\dfrac{n + 1}{2}\Big)^{\text{th term}} = \dfrac{5 + 1}{2} = \dfrac{6}{2}$ = 3rd term = 12.

Given,

Mean = Median

$\therefore \dfrac{8 + 10 + 12 + x + 15}{5}$ = 12

⇒ 45 + x = 60

⇒ x = 60 - 45 = 15.

By formula,

If the number of observations is n, their mean = $\dfrac{\text{Sum of observations}}{n}$ and median (if n is odd) = value of the $\Big(\dfrac{n + 1}{2}\Big)^{\text{th}}$ observation.

∴ A and R both are true.

Hence, Option 1 is the correct option.