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  1. The count() aggregation function counts only non-null values. To count all values, whether null or non-null, use size.

  2. You can specify the names of aggregated columns as the arguments to the agg function. Here I use a dictionary so that I can use string constants for colum names.

    # Series level
    df.groupby("class")["sepal length (cm)"].agg(
            # 'new column': 'function',
            "sepal_average_length": "mean",
            "sepal_standard_deviation": "std",
    # DataFrame level
            # 'new column': ('column', 'function'),
            "sepal_average_length": ("sepal length (cm)", "mean"),
            "sepal_standard_deviation": ("sepal length (cm)", "std"),

Via Christopher Tao and Soner Yıldırım.