Properties of Sigma Notation

Sigma notation is a notation used to express the sum. The sigma notation is symbolized by ∑.
Sigma Notation
The purpose of the above sigma formula is the sum of all X data starting from the order of 1 to n. If exemplified by the amount of data n = 5, the sigma formula obtained is:
Note:   Sigma Capital

             i = 1   => lower limit
             i = n   => upper limit
The above description we conclude the values ​​of observations for variable X which is added from the first observation to the fifth observation ..

Properties of Sigma Notation


If c is a constant, then 



The proof is by decomposing the left side and then factoring, obtained;
If c is a constant and all data X is 1, then
Proof: If in nature all values ​​of Xi are equal to 1, then
The sum of the two or more variables is equal to the sum of each of them, so
The proof:
By decomposing the left side and then regrouping, we get:
Not infrequently, we encounter data classified according to two criteria. For example, Xij represents the amount of gas produced if a particular chemical experiment is carried out at the temperature level i and the pressure level j.
To add up such power, it is very easy if we use double summing notation.
then we first add up according to the subscript j, following the single addition rule, and then do the second addition with i taking values ​​from 1 to m. Thus, for the data in the following table;


Pressure
1
2
3
4
Temperature
1
X11
X12
X13
X14
2
X21
X22
X23
X24

We get,



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