The less-than ogive plots each class's upper boundary against its running cumulative frequency; the median is the marks-value where the cumulative frequency first reaches N/2 = 30 on this curve.

Step 1 — Build the less-than cumulative frequency table.

Check: $5+8+15+20+8+4=60$ students in total, matching the given cumulative frequency of $60$ at the last point — confirms the table.

Step 2 — Draw the less-than ogive. Plot $(10,5), (20,13), (30,28), (40,48), (50,56), (60,60)$ and join consecutively with straight line segments; the curve should also start at $(0,0)$, since no student can score less than 0.

Step 3 — Locate $N/2$ on the curve. $N=60$, so $N/2=30$. This value lies between the plotted points $(30,28)$ and $(40,48)$ — i.e. on the straight segment joining them.

Step 4 — Read off (compute) the corresponding marks-value. Along that segment, cumulative frequency rises by $48-28=20$ as marks rise by $40-30=10$, a rate of $20/10=2$ per mark. To rise from $28$ to $30$ (an increase of $2$) needs $2/2=1$ extra mark beyond $30$. So the median is at marks $=30+1=31$. …

The median can equally be found as the X-coordinate where the less-than ogive and the more-than ogive (built from the more-than cumulative frequencies 60, 55, 47, 32, 12, 4) intersect — both …

Reading the median straight off the ogive at cumulative frequency $N=60$ (the top of the curve) instead of $N/2=30$ (its halfway point) is the most common error. Forgetting that the less-than ogive uses UPPER clas …