Assertion (A) : Lower quartile for the data 9, 11, 15, 19, 17, 13, 7 is 9.

Reason (R) : For finding quartiles, the given data are arranged in descending order of their magnitudes, then lower quartile (Q₁) = $\Big(\dfrac{n}{4}\Big)^{\text{th}} \text{ term or } \Big(\dfrac{n + 1}{4}\Big)^{\text{th}} \text{ term }$, depending whether n is even or 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.

Data : 9, 11, 15, 19, 17, 13, 7

Arranging the data in ascending order, we get :

7, 9, 11, 13, 15, 17, 19.

Since, n = 7, which is odd.

By formula,

Lower quartile = $\Big(\dfrac{n + 1}{4}\Big)^{th} \text{ term } = \dfrac{7 + 1}{4} = \dfrac{8}{4}$

= 2nd term = 9.

∴ Assertion (A) is true.

For finding quartiles, the given data are arranged in ascending order of their magnitudes, then lower quartile (Q₁) = $\Big(\dfrac{n}{4}\Big)^{\text{th}} \text{ term or } \Big(\dfrac{n + 1}{4}\Big)^{\text{th}} \text{ term }$, depending whether n is even or odd.

∴ Reason (R) is false.

Hence, Option 1 is the correct option.