To follow your idea of creating an array and getting the median this way:
In [235]: df
Out[235]:
Female Male
age
78 9.0 12.0
79 13.0 4.0
80 10.0 7.0
81 8.0 6.0
82 4.0 5.0
In [236]: df = df.astype(int)
In [237]: df
Out[237]:
Female Male
age
78 9 12
79 13 4
80 10 7
81 8 6
82 4 5
In [238]: df = df.reset_index('age')
In [240]: df = df.melt(id_vars='age', var_name='gender', value_name='count')
In [241]: df
Out[241]:
age gender count
0 78 Female 9
1 79 Female 13
2 80 Female 10
3 81 Female 8
4 82 Female 4
5 78 Male 12
6 79 Male 4
7 80 Male 7
8 81 Male 6
9 82 Male 5
In [242]: df['age'] = df.apply(lambda s: [s['age']] * s['count'], axis=1)
In [243]: df
Out[243]:
age gender count
0 [78, 78, 78, 78, 78, 78, 78, 78, 78] Female 9
1 [79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 7... Female 13
2 [80, 80, 80, 80, 80, 80, 80, 80, 80, 80] Female 10
3 [81, 81, 81, 81, 81, 81, 81, 81] Female 8
4 [82, 82, 82, 82] Female 4
5 [78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78] Male 12
6 [79, 79, 79, 79] Male 4
7 [80, 80, 80, 80, 80, 80, 80] Male 7
8 [81, 81, 81, 81, 81, 81] Male 6
9 [82, 82, 82, 82, 82] Male 5
In [245]: df = df.explode('age')
In [249]: df['age'] = df['age'].astype(int)
In [251]: df
Out[251]:
age gender count
0 78 Female 9
0 78 Female 9
0 78 Female 9
0 78 Female 9
0 78 Female 9
.. ... ... ...
9 82 Male 5
9 82 Male 5
9 82 Male 5
9 82 Male 5
9 82 Male 5
[78 rows x 3 columns]
In [250]: df.groupby('gender')['age'].median()
Out[250]:
gender
Female 79.5
Male 80.0
Name: age, dtype: float64