A 'less than' table for the heights (in cm) of 200 army recruits:
less than 150 -> 15, less than 160 -> 62, less than 170 -> 128, less than 180 -> 180, less than 190 -> 200.
In which class does the median height lie?

A 'less than' column IS the cumulative frequency column, so no conversion is needed just to locate the median class: $n=200$ (the last entry) and $\frac{n}{2}=100$. The first entry to reach 100 is 128, recorded against the boundary 170, so the median lies in 160-170. 150-160 is the row whose cf (62) is still below 100 — it supplies cf, not the class. 170-180 is one row too far, and 180-190 is where the count reaches $n$ rather than $\frac{n}{2}$. The ordinary frequencies 15, 47, 66, 52, 20 are only needed once you want f for the formula.