# numpy.average

numpy.average(a, axis=None, weights=None, returned=False)

  Compute the weighted average along the specified axis.

  Parameters
    a array_like

      Array containing data to be averaged. If a is not an array, a conversion is attempted.

    axis None or int or tuple of ints, optional

      Axis or axes along which to average a. The default, axis=None, will average over all of the elements of the input array. If axis is negative it counts from the last to the first axis.

      New in version 1.7.0.

      If axis is a tuple of ints, averaging is performed on all of the axes specified in the tuple instead of a single axis or all the axes as before.

    weights array_like, optional

      An array of weights associated with the values in a. Each value in a contributes to the average according to its associated weight. The weights array can either be 1-D (in which case its length must be the size of a along the given axis) or of the same shape as a. If weights=None, then all data in a are assumed to have a weight equal to one. The 1-D calculation is:

          avg = sum(a * weights) / sum(weights)

      The only constraint on weights is that sum(weights) must not be 0.

    returned bool, optional

      Default is False. If True, the tuple (`average`, sum_of_weights) is returned, otherwise only the average is returned. If weights=None, sum_of_weights is equivalent to the number of elements over which the average is taken.

  Returns
    retval, [sum_of_weights]array_type or double

      Return the average along the specified axis. When returned is True, return a tuple with the average as the first element and the sum of the weights as the second element. sum_of_weights is of the same type as retval. The result dtype follows a genereal pattern. If weights is None, the result dtype will be that of a , or `float64` if a is integral. Otherwise, if weights is not None and a is non- integral, the result type will be the type of lowest precision capable of representing values of both a and weights. If a happens to be integral, the previous rules still applies but the result dtype will at least be `float64`.

  Raises
    ZeroDivisionError

      When all weights along axis are zero. See `numpy.ma.average` for a version robust to this type of error.

    TypeError

      When the length of 1D weights is not the same as the shape of a along axis.

  See also

  `mean`
  `ma.average`

    average for masked arrays – useful if your data contains “missing” values

  `numpy.result_type`

    Returns the type that results from applying the numpy type promotion rules to the arguments.

  Examples

      >>> data = np.arange(1, 5)
      >>> data
      array([1, 2, 3, 4])
      >>> np.average(data)
      2.5
      >>> np.average(np.arange(1, 11), weights=np.arange(10, 0, -1))
      4.0

      >>> data = np.arange(6).reshape((3,2))
      >>> data
      array([[0, 1],
             [2, 3],
             [4, 5]])
      >>> np.average(data, axis=1, weights=[1./4, 3./4])
      array([0.75, 2.75, 4.75])
      >>> np.average(data, weights=[1./4, 3./4])
      Traceback (most recent call last):
          ...
      TypeError: Axis must be specified when shapes of a and weights differ.

      >>> a = np.ones(5, dtype=np.float128)
      >>> w = np.ones(5, dtype=np.complex64)
      >>> avg = np.average(a, weights=w)
      >>> print(avg.dtype)
      complex256

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