The same as :func:`weighted_mean`, except the argument is expected to be a
   two-column :class:`pandas.DataFrame` whose first column gives the data
   values and second column gives their uncertainties. Returns
   ``(weighted_mean, uncertainty_in_mean)``.

def weighted_mean_df (df, **kwargs):
    """The same as :func:`weighted_mean`, except the argument is expected to be a
   two-column :class:`pandas.DataFrame` whose first column gives the data
   values and second column gives their uncertainties. Returns
   ``(weighted_mean, uncertainty_in_mean)``.

    """
    return weighted_mean (df[df.columns[0]], df[df.columns[1]], **kwargs)