docs: def weighted_variance (x, weights):
      """Return the variance of a weighted sample.
  
      The weighted sample mean is calculated and subtracted off, so the returned
      variance is upweighted by ``n / (n - 1)``. If the sample mean is known to
      be zero, you should just compute ``np.average (x**2, weights=weights)``.
  
      """
      n = len (x)
      if n < 3:
          raise ValueError ('cannot calculate meaningful variance of fewer '
                            'than three samples')
      wt_mean = np.average (x, weights=weights)
      return np.average (np.square (x - wt_mean), weights=weights) * n / (n - 1)