For the distribution 10-20 -> 7, 20-30 -> 13, 30-40 -> 18, $40-50->12(n=50)$ a student writes Median = $35+((25-20)/18)\times 10=37.78$. What went wrong, and what is the correct median?

Cumulative frequencies 7, 20, 38, 50 give $n=50$ and $\frac{n}{2}=25$, so the median class is 30-40. His cf = 20 and $f=18$ are both correct; the only wrong ingredient is l, where he used the class MARK $\frac{30+40}{2}=35$ instead of the lower boundary 30. The correct value is $30+\left(\frac{25-20}{18}\right)\times 10=32.78$, and his answer is exactly 5 too big — the same 5 by which 35 exceeds 30. For reference, the other two mistakes listed would have given 22.78 (using cf = 38) and 33.85 (using $f=13$).