how to use arithmetic operations in groupby function and assign the result to existed dataframe in pandas

suppose I have following dataframe:

data = {'id':[1,1,2,2,2,3,3,3],
                  'var':[10,12,8,11,13,14,15,16],
                  'ave':[2,2,1,4,3,5,6,8]}
df = pd.DataFrame(data)

I am trying to have the operation, con = var*((ave)/sum(ave)), based on each id and then assign the result to my existed dataframe.
by the code below I have tried to define my operation but still do not know what is the problem.

df =df["id"].map( df.groupby(['id']).
                               apply(lambda x: x[var]*(x[ave])/x[ave].sum())

my expected output would be like this:

    id   var   ave   con
1     1    10     2  5   
2     1    12     2  6   
3     2     8     1  1   
4     2    11     4  5.5 
5     2    13     3  4.88
6     3    14     5  3.68
7     3    15     6  4.74
8     3    16     8  6.74

thank you in advance.

>Solution :

Don’t use apply, use a vectorial expression with groupby.transform('sum'):

df['con'] = df['var'].mul(df['ave'].div(df.groupby('id')['ave'].transform('sum')))

# or
# df['con'] = df['var']*df['ave']/df.groupby('id')['ave'].transform('sum')

Output:

   id  var  ave       con
0   1   10    2  5.000000
1   1   12    2  6.000000
2   2    8    1  1.000000
3   2   11    4  5.500000
4   2   13    3  4.875000
5   3   14    5  3.684211
6   3   15    6  4.736842
7   3   16    8  6.736842