The less than ogive (blue) and the more than ogive (violet) for the homework time of 50 students are drawn on the same graph. They cross at the point P. What is the median homework time?

**Less-than ogive**: plot points (upper limit of class, cf) for each class. Connect with smooth curve.

**More-than ogive**: plot points (lower limit of class, more-than-cf). Connect smoothly.

**Median from ogives**:
- Method A: From the less-than ogive, find where cf = $n/2$. Drop perpendicular to $x$-axis. The $x$-coordinate is the median.
- Method B: Plot BOTH ogives on the same axes. Their intersection's $x$-coordinate is the median.

**Empirical relationship** (rough): Mode ≈ 3 × Median − 2 × Mean. Useful sanity check, not rigorously true but often close.

**Frequency polygon vs ogive**: Polygon plots (class mark, frequency); Ogive plots (limit, cumulative frequency).