How to do feature analyzing : pandas groupby(). mean
Means are calculated just to have an idea of the relationship. For more definite analysis, one can use simple statistics to know relationship between two variables. The test to be applied depends on type of variables: 

If both are numeric: Correlation (Pearson or Spearman)

If both are grouping (nominal) variables: Chi-square test
   Fisher exact test can also be used if only 2 groups in each variable.

If one is grouping and other numeric: 
   if only 2 groups: Student t-test or Mann-Whitney U test
   if more than 2 groups: ANOVA or Kruskal–Wallis test


Means of different groups will give you only partial information about relationship. However, it may be sufficient to know if the feature is likely to be important for prediction. As a method of feature selection, if groups' mean do not differ significantly, this feature may be dropped from analysis.