WeightedMean-v1.rst

.. algorithm::

.. summary::

.. alias::

.. properties::

Description
-----------

The algorithm calculates the weighted mean of two workspaces. This is useful when working with distributions rather than histograms, particularly when counting statistics are poor and it is possible that the value of one data set is statistically insignificant but differs greatly from the other. In such a case simply calculating the average of the two data sets would produce a spurious result. This algorithm will eventually be modified to take a list of workspaces as an input.

:math:`y=\frac{\sum\frac{x_i}{\sigma^{2}_i}}{\sum\frac{1}{\sigma^{2}_i}}`

Usage
-----

**Example - Perform a simple weighted mean**

.. testcode:: ExWMSimple

    # create histogram workspaces
    dataX1 = [0,1,2,3,4,5,6,7,8,9] # or use dataX1=range(0,10)
    dataY1 = [0,1,2,3,4,5,6,7,8] # or use dataY1=range(0,9)
    dataE1 = [1,1,1,1,1,1,1,1,1] # or use dataE1=[1]*9
    dataX2 = [1,1,1,1,1,1,1,1,1,1]
    dataY2 = [2,2,2,2,2,2,2,2,2]
    dataE2 = [3,3,3,3,3,3,3,3,3]
    ws1 = CreateWorkspace(dataX1, dataY1, dataE1)
    ws2 = CreateWorkspace(dataX2, dataY2, dataE2)

    # perform the algorithm
    ws = WeightedMean(ws1, ws2)

    print "The X values are: " + str(ws.readX(0))
    print "The Y values are: " + str(ws.readY(0))
    print "The E values are: " + str(ws.readE(0))

Output:

.. testoutput:: ExWMSimple

    The X values are: [ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9.]
    The Y values are: [ 0.2  1.1  2.   2.9  3.8  4.7  5.6  6.5  7.4]
    The E values are: [ 0.9486833  0.9486833  0.9486833  0.9486833  0.9486833  0.9486833
      0.9486833  0.9486833  0.9486833]

.. categories::

.. sourcelink::