Q.Find the median (second quartile $Q_2$) of the discrete distribution: $x = 1, 2, 3, 4, 5$ with frequencies $f = 3, 5, 8, 6, 3$.

Build the $cf$ column ($N = 25$) and locate the $Q_2$ position $\frac{2(N+1)}{4} = \frac{N+1}{2}$.

Form the less-than cumulative frequency column:

$N = 25$, $N + 1 = 26$. The $Q_2$ position is $\dfrac{2(26)}{4} = \dfrac{26}{2} = 13$.

The first $cf \ge 13$ is $16$, against $x = 3$. Therefore $Q_2 = 3$. …

Counting directly: $8$ observations have $x \le 2$ and $16$ have $x \le 3$, so the middle (13th of 25) observation is a $3$ — the …

Reading $x = 2$ because its $cf$ ($8$) is the last value below $13$. The rule selects the first $cf$ that rea …