Properties of Sigma Notation
Sigma
notation is a notation used to express the sum. The sigma notation is
symbolized by ∑.
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:
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 ..
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, X_{ij} 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

X_{11}

X_{12}

X_{13}

X_{14}

2

X_{21}

X_{22}

X_{23}

X_{24}

We
get,
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