Assertion (A) : The third quartile of the data 1, 20, 3, 15, 6, 8, 13, 5, 21, 23, 17, 10, 9, 12, 18, 21 is 18

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

Q₃ = $\dfrac{\text{3n}}{4} + 1$ th observation, if n is even.

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

Observations arranging in ascending order = 1, 3, 5, 6, 8, 9, 10, 12, 13, 15, 17, 18, 20, 21, 21, 23

Here, n = 16

We know that,

If the variates are arranged in ascending order, then the observation lying midway between the median and the upper extreme is called the Upper quartile or Third quartile.

Q₃ = $\dfrac{3\text{n}}{4}$ th observation, if n is even.

= $\dfrac{3 \times 16}{4} = \dfrac{48}{4}$ = 12 th observation = 18.

∴ Assertion (A) is true.

For an ungrouped data, containing n observations, upper quartile is given by,

Q₃ = $\dfrac{3\text{n}}{4}$ th observation, if n is even.

∴ Reason (R) is false.

Hence, Option 1 is the correct option.