Pandas: remove group from the data when a value in the group meets a required condition

Based on what you described in the question, as long as there is at least one value is below 8 within the group, then that group should be dropped. So the equivalent statement is that as long as the minimum value within that group is below 8, that group should be dropped.

By using the filter feature, the actual code can be reduced to only one line, please refer to Filtration, you may use the following code:

dfnew = df.groupby('Groups').filter(lambda x: x['Count'].min()>8 )
dfnew.reset_index(drop=True, inplace=True) # reset index
dfnew = dfnew[['Groups','Count']] # rearrange the column sequence
print(dfnew)

Output:
   Groups  Count
0       2     12
1       2     15
2       2     21

You can use isin, loc and unique with selecting subset by inverted mask. Last you can reset_index:

print df

  Groups  Count
0       1      7
1       1     11
2       1      9
3       2     12
4       2     15
5       2     21

print df.loc[df['Count'] < 8, 'Groups'].unique()
[1]

print ~df['Groups'].isin(df.loc[df['Count'] < 8, 'Groups'].unique())

0    False
1    False
2    False
3     True
4     True
5     True
Name: Groups, dtype: bool

df1 = df[~df['Groups'].isin(df.loc[df['Count'] < 8, 'Groups'].unique())]
print df1.reset_index(drop=True)

   Groups  Count
0       2     12
1       2     15
2       2     21