For 90 observations grouped in classes of width 25, a student writes Median = 75 + (45 - 38)/21 = 75.33. His median class is correctly identified, with l = 75, cf = 38 and f = 21. What is the correct median?

The factor $h=25$ has been left out. Median = $75+\left(\frac{45-38}{21}\right)\times 25=75+\frac{7}{21}\times 25=75+8.33=83.33$. Note the check that would have caught it: $\frac{n/2-cf}{f}=\frac{1}{3}$ is a FRACTION of the class, so it must be multiplied by the class width before being added to l — an answer of 75.33 barely moves off the lower boundary of a class 25 units wide. 100.33 adds $h$ instead of multiplying by it, and 66.67 swaps $\frac{n}{2}$ and $cf$ in the numerator.