The marks of 60 students are grouped in classes of width 10 and the median comes out as 47.5. The very same marks are now regrouped into classes of width 20 (0-20, 20-40, 40-60, ...). The median computed from the new table will:

The formula Median = $l+\left(\frac{n/2-cf}{f}\right)\times h$ assumes the observations are spread EVENLY across the median class. Widening the classes changes which observations share a class, so that even-spread assumption is applied differently and the interpolated value usually moves a little. It is an estimate of the true median, never the true median itself. It cannot double or halve, because the answer must still lie inside the new median class, which covers the same marks. The two groupings agree exactly only in the special case where the data really is uniformly spread inside every class.