Tools to explore various datasets
There is a very cool active Python package called pandas-profiling, is exactly what you want. With a simple pandas_profiling.ProfileReport(df) it returns a lot of important statistical information about your data, the official documentation says:


  For each column the following statistics - if relevant for the column
  type - are presented in an interactive HTML report:
  
  
  Essentials: type, unique values, missing values 
  Quantile statistics like minimum value, Q1, median, Q3, maximum, range, interquartile    range 
  Descriptive statistics like mean, mode, standard deviation,    sum, median absolute deviation, coefficient of variation, kurtosis,
  skewness Most frequent values 
  Histogram 
  Correlations highlighting of highly correlated variables, Spearman and Pearson matrixes
  


Look at their demo here.
I personally used it few times and it quite nice, BUT it dataset is large (mostly I mean in variable space) it takes a long time to give the statistics. I think there should be an option to even return all these statistics for a subset of features (columns) in case you do not want for all and it is very high dimensional!