Use summation notation to express the sum of all numbers

Use summation notation to express the sum of a subset of numbers

Use summation notation to express the sum of squares

If  we have a variable X that represents the weights (in grams) of 4 grapes. The data are shown in Table 1. Table 1. Weights of 4 grapes.

GrapeX
1
2
3
4
4.6
5.1
4.9
4.4

We label Grape 1’s weight X1, Grape 2’s weight X2, etc. The following formula means to sum up the weights of the four grapes:

http://onlinestatbook.com/2/introduction/graphics/summation1.gif

The Greek letter capital sigma (Σ) demonstrates summation. The “I = 1” at the base demonstrates that the summation is to begin with X1 and the 4 at the top shows that the summation will end with X4. The “Xi” demonstrates that X is the variable to be added as I goes from 1 to 4. In this way,

http://onlinestatbook.com/2/introduction/graphics/summation1.gif

= X1 + X2 + X3 + X4 = 4.6 + 5.1 + 4.9 + 4.4 = 19.0.

The symbol

http://onlinestatbook.com/2/introduction/graphics/summation1.gif

shows that lone the initial 3 scores are to be added. The list variable I goes from 1 to 3. 

At the point when every one of the scores of a variable, (for example, X) are to be added, it is frequently advantageous to utilize the accompanying abridged documentation:

http://onlinestatbook.com/2/introduction/graphics/summation3.gif

In this manner, when no estimations of I are appeared, it intends to aggregate every one of the estimations of X. 

Numerous recipes include squaring numbers before they are added. This is shown as

ΣX² = 4.62 + 5.12 + 4.92 + 4.42 = 21.16 + 26.01 + 24.01 + 19.36 = 90.54.

http://onlinestatbook.com/2/introduction/graphics/sum5.gif

Notice that:

since the articulation on the left way to summarize every one of the estimations of X and after that square the entirety (19² = 361), while the articulation on the correct way to square the numbers and after that aggregate the squares (90.54, as appeared). 

A few recipes include the aggregate of cross items. Table 2 shows the information for factors X and Y. The cross items (XY) are appeared in the third segment. The total of the cross items is 3 + 4 + 21 = 28.

Table 2. Cross Products.

XYXY
1
2
3
3
2
7
3
4
21

In summation notation, this is written as: ΣXY = 28.