THE average weighted is one of measures Statistics responsible for representing large lists of information through just one number.
Example of using averaging:
Suppose Brazilians consume, in average, 42 kilos of rice per year. This is not to say that the consumption of each is exactly 42 kg of rice, but that some consume more than that and others less, so that producers need to account for 42 kilos of rice for each Brazilian every years old. Therefore, the number that really matters for the production is the average.
Weighted Average Calculation
O degreeinimportance of each number in one averageweighted is represented by a Weight. The following situation demonstrates how these weights work: if a teacher applies two tests during his course and the second test is worth three times more than the first, in this case, we say that the first test has weight 1 and the second has weight 3.
To calculate the averagepondered, observe the following guidelines:
Multiply the information that needs to be averaged by their respective weights;
2 – Add the results of these multiplications;
3 – Divide the result obtained by the sum of the weights used.
Mathematically, it is possible to represent each Weight by P1, P2… and each information by N1, no2… So, we will have the averageweighted M through the following expression:
M = P1N1 + P2N2 + … + PiNi
P1 + P2 + … + Pi
Examples
1st Example – A teacher managed to make his most important tests the last by assigning weights different for each. The first test had weight 1; the second, weight 3; and the third, weight 5. One of the students got the following grades: 7.0 on the first test; 6.0 in the second and 4.0 in the third. This student will be able to achieve the average final 6.0 required by the school?
Solution:
To solve this problem, we can use the weighted average formula up to “index 3”.
M = P1N1 + P2N2 + P3N3
P1 + P2 + P3
M = 1·7 + 3·6 + 5·4
1 + 3 + 5
M = 7 + 18 + 20
9
M = 45
9
M = 5
Note that when assigning biggerimportance to the last tests, the teacher gave a higher value to them than to the first one, although all tests had a value between 0 and 10 in the correction. Also note that even getting two grades above the average, the student failed to reach the final grade of the school. This happened because the first two tests were worth less than the last one, in which he got the lowest grade.
2ºExample – A shoe store purchased the following materials to manufacture its products: 160 meters of leather, 200 packs of nails and 40 hammers. Knowing that each meter of leather costs R$23.00; each package of nail costs BRL 13.90 and each hammer costs BRL 15.50, calculate the spentaverage of the company by product purchased.
Solution:
Consider that the quantities of each material are yours. weights:
M = P1N1 + P2N2 + P3N3
P1 + P2 + P3
M = 160·23 + 200·13,90 + 40·15,5
160 + 200 + 40
M = 3680 + 2780 + 620
400
M = 6780
400
M = 16.95
In average, R$ 16.95 were spent per material purchased.
By Luiz Paulo Moreira
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-media-ponderada.htm