Revert "Revert "Updated error propagation page. re #9690""

This reverts commit b637b9c.

Code/Mantid/docs/source/algorithms/BinaryOperation.txt

@@ -10,6 +10,8 @@ Workspaces are compatible if:
 * the units of the axes match
 * the distribution status/counts units match
 
+For information about how errors are handled and propagated see :ref:`Error Propagation`.
+
 Compatible Sizes
 ################
 

Code/Mantid/docs/source/concepts/Error_Propagation.rst

@@ -9,45 +9,43 @@ Propogation and how it is used in its algorithms.
 Theory
 ------
 
-In order to deal with error propagation, Mantid treats errors as a
-guassian curve (also known as a bell curve or normal curve). Meaning
-that if X = 100 +- 1 then it is still possible for a value of 102 to
-occur, but far less likely than 101 or 99, then a value of 105 is far
-less likely still than 102, and then 110 is simply unheard of.
-
-This allows Mantid to work with the errors quite simply.
+In order to deal with error propagation, Mantid treats errors as guassian 
+probabilities (also known as a bell curve or normal probabilities) and each 
+observation as independent. Meaning that if X = 100 +- 1 then it is still 
+possible for a value of 102 to occur, but less likely than 101 or 99, and a 
+value of 105 is far less likely still than any of these values.
 
 Plus and Minus Algorithm
 ------------------------
 
-The plus algorithm adds a selection of datasets together, including
-their margin of errors. Mantid has to therefore adapt the margin of
-error so it continues to work with just one margin of error. The way it
-does this is by simply adding together the certain values, for this
-example we will use X\ :sub:`1` and X\ :sub:`2`. X\ :sub:`1` = 101 ± 2
-and X\ :sub:`2` = 99 ± 2, Just to make it easier. Mantid takes the
-average of the two definite values, 101 and 99.
+The plus algorithm adds a selection of datasets together, including their 
+margin of errors. Mantid has to therefore adapt the margin of error so it 
+continues to work with just one margin of error. The way it does this is by 
+simply adding together the certain values. Consider the example where: 
+X\ :sub:`1` = 101 ± 2 and X\ :sub:`2` = 99 ± 2. Then for the Plus algorithm
 
 X = 200 = (101 + 99).
 
-The average of the error is calculated by taking the root of the sum of
-the squares of the two error margins:
+The propagated error is calculated by taking the root of the sum of the 
+squares of the two error margins:
 
 (√2:sup:`2` + 2\ :sup:`2`) = √8
 
+Hence the result of the Plus algorithm can be summarised as:
+
 X = 200 ± √8
 
-Mantid deals with the minus algorithm similarly, doing the inverse
-function of Plus.
+Mantid deals with the Minus algorithm similarly.
 
 Multiply and Divide Algorithm
 -----------------------------
 
 The Multiply and Divide Algorithm work slightly different from the Plus
-and Minus Algorithms, in the sense that they have to be more complex.
+and Minus Algorithms, in the sense that they have to be more complex, 
+see also `here <http://en.wikipedia.org/wiki/Propagation_of_uncertainty>`_.
 
 To calculate error propagation, of say X\ :sub:`1` and X\ :sub:`2`.
-X\ :sub:`1` = 101 ± 2 and X\ :sub:`2` = 99 ± 2 again, Mantid would
+X\ :sub:`1` = 101 ± 2 and X\ :sub:`2` = 99 ± 2 ,Mantid would
 undertake the following calculation for divide:
 
 Q = X\ :sub:`1`/X:sub:`2` = 101/99