def standardize(df):
    """
    Fill in this function to standardize each column of the given
    DataFrame. To standardize a variable, convert each value to the
    number of standard deviations it is above or below the mean.
    
    This time, try to use vectorized operations instead of apply().
    You should get the same results as you did before.
    """
    # return df.sub(df.mean(), axis='columns').div(df.std(ddof=0), axis='columns')
    return (df - df.mean()) / df.std(ddof=0)