For the list of $16$ numbers $2$, $4$, $4$, $5$, $7$, $7$, $7$, $7$, $7$, $8$, $8$, $9$, $9$, $9$, $9$, $9$ (already sorted), what are the **first and third quartiles** $Q_1$ and $Q_3$? (Use the convention that $Q_1$ is the median of the lower half and $Q_3$ is the median of the upper half.)

$n = 16$, so split into two halves of 8 each: - Lower half (1st–8th): $2, 4, 4, 5, 7, 7, 7, 7$. - Upper half (9th–16th): $7, 8, 8, 9, 9, 9, 9, 9$. **$Q_1$** = median of the lower half. With 8 numbers the median is the average of the 4th and 5th: $\dfrac{5 + 7}{2} = 6$. **$Q_3$** = median of the upper half. Average of the 4th and 5th values of the upper group: $\dfrac{8 + 9}{2} = 8.5$. So $Q_1 = 6$, $Q_3 = 8.5$. Trap A simply picks the first and last values. Trap C/D use the wrong averaging — common when students take the 4th value alone rather than the (4th + 5th)/2.