With $N=30$ (an even number of students), the median needs the 15th and 16th observations, found from a cumulative frequency table.

Since $N = \sum f = 30$ is even, the median is the average of the $\left(\dfrac{N}{2}\right)$-th $= 15$th and the $\left(\dfrac{N}{2}+1\right)$-th $= 16$th observations, located using the cumulative frequency column.

Step 1 — Build the cumulative frequency table.

Check: $\sum f = 2+5+8+7+5+3 = 30$, matching the given total of 30 students.

Step 2 — Locate the 15th and 16th observations. The c.f. reaches exactly 15 at $x=5$, meaning observations numbered 8 through 15 all equal 5 (since the previous c.f., at $x=4$, was 7). So the 15th observation is 5. The c.f. reaches 22 at $x=6$, meaning observations 16 through 22 all equal 6. So the 16th observation is 6.

Step 3 — Average the two middle observations. …

Reading the median straight off the c.f. column as "the value where c.f. equals $N/2$" without checking whether $N$ is odd or even is the most common error — here that shortcut would wrongly stop at $x=5$ instead of correctly averaging with the next value, …