Assertion (A): If 6 students score 78, 62, 91, 37, 80 and 66 marks in a subject, then median score is 72.

Reason (R): If number of observations is even, then

Median = $\dfrac{\dfrac{n}{2}\text{th observation} + \Big(\dfrac{n}{2} + 1\Big)\text{th observation}}{2}$, after putting all observations in ascending or descending order.

1. Assertion (A) is true, Reason (R) is false.

2. Assertion (A) is false, Reason (R) is true.

3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

According to assertion: if 6 students score 78, 62, 91, 37, 80 and 66 marks in a subject, then median score is 72.

Arrange the scores in ascending order: 37, 62, 66, 78, 80, 91

There are 6 scores, so n = 6. This is an even number.

If number of observations is even, then

Median = $\dfrac{\dfrac{n}{2}\text{th observation} + \Big(\dfrac{n}{2} + 1\Big)\text{th observation}}{2}$, after putting all observations in ascending or descending order.

∴ Reason (R) is true.

Substituting the value,

$\text{Median }= \dfrac{\dfrac{6}{2}\text{th observation} + \Big(\dfrac{6}{2} + 1\Big)\text{th observation}}{2}\\[1em] = \dfrac{3\text{rd observation} + (3 + 1)\text{th observation}}{2}\\[1em] = \dfrac{3\text{th observation} + 4\text{th observation}}{2}\\[1em] = \dfrac{66 + 78}{2}\\[1em] = \dfrac{144}{2}\\[1em] = 72.$

∴ Assertion (A) is true.

∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.