Every frequency in a grouped table is doubled, so each class now holds twice as many observations. The class boundaries are unchanged. The median of the distribution:

Doubling every frequency doubles $n$, so $\frac{n}{2}$ doubles; every cumulative frequency doubles too, so the SAME class is still the median class. In Median = $l+\left(\frac{n/2-cf}{f}\right)\times h$ the numerator and the denominator are both doubled, so the fraction is unchanged, and $l$ and $h$ never depended on the frequencies at all. The median therefore stays exactly where it was. It would double only if every class boundary doubled, and it shifts by $h$ only if every boundary shifts by $h$.