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python - Pandas: How to fill null values with mean of a groupby?

I have a dataset will some missing data that looks like this:

id    category     value
1     A            NaN
2     B            NaN
3     A            10.5
4     C            NaN
5     A            2.0
6     B            1.0

I need to fill in the nulls to use the data in a model. Every time a category occurs for the first time it is NULL. The way I want to do is for cases like category A and B that have more than one value replace the nulls with the average of that category. And for category C with only single occurrence just fill in the average of the rest of the data.

I know that I can simply do this for cases like C to get the average of all the rows but I'm stuck trying to do the categorywise means for A and B and replacing the nulls.

df['value'] = df['value'].fillna(df['value'].mean()) 

I need the final df to be like this

id    category     value
1     A            6.25
2     B            1.0
3     A            10.5
4     C            4.15
5     A            2.0
6     B            1.0
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I think you can use groupby and apply fillna with mean. Then get NaN if some category has only NaN values, so use mean of all values of column for filling NaN:

df.value = df.groupby('category')['value'].apply(lambda x: x.fillna(x.mean()))
df.value = df.value.fillna(df.value.mean())
print (df)
   id category  value
0   1        A   6.25
1   2        B   1.00
2   3        A  10.50
3   4        C   4.15
4   5        A   2.00
5   6        B   1.00

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