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Weighted Average

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It is known as average to figure that results identical or what is the nearest to arithmetic average . The average can also be the point at which a thing is divided in the middle.

The notion of weighted average is used to name a calculation method which is applied when, within a series of data, one of them has a major importance . There is, therefore, a fact with greater weight than the rest The weighted average consists of establishing said weight, also known as weighing , and use that value to calculate the average.

With this clear, we can understand how the weighted average is calculated. First we must multiply each fact by their weighting and then add those values. Finally we must divide this sum by the sum of all weights.

The most common use of this calculation is linked to certain evaluations . Assume that, to complete a certain course , a student must take five current exams and a final exam that is equivalent to the other five exams. This means that, if each current exam has a weighting of 1 , the final exam will have a weighting of 5 .

The student in question obtains the following marks: 6 , 7 , 5 , 7 and 8 in the current exams and 6 in the final exam. Appealing to the formula already mentioned, the weighted average of this student's grades will be equal to the sum of each one multiplied by its weighting (6 x 1 + 7 x 1 + 5 x 1 + 7 x 1 + 8 x 1 + 6 x 5 = 63 ) divided by the sum of all weights (1 + 1 + 1 + 1 + 1 + 5 = 10 ). The weighted average in this case, therefore, is 6,3 .

The importance of the weighted average may not be obvious but, on the contrary, it is a technique very useful and that can make a considerable difference with the calculation of the normal average. Returning to the example set out in the previous paragraph, which reflects one of the most common applications of the weighted average in the life of university students, let's see what would happen if the weight of each data were not taken into account : If we simply added the six grades and divided them by six, the result we would obtain would be 6.5.

Between 6.3 and 6.5 the difference may seem insignificant, but the same would not happen if the minimum qualification to pass was the latter; in such case, to proceed incorrectly to calculate the average (that is, by overlooking the weight of each data and simply performing the average) would lead the student to think that he has passed the exam successfully, despite not being true. If the last exam were more extensive and had a weight four times greater (20), the distance between the two results it would be truly considerable, since the weighted average would give 4.65.

What advantage does a teacher offer the existence of the weighted average when preparing a series of assessments? Could you examine your students on the same subjects if you did not have this technique to calculate their grades? The main benefit is the possibility of Group more than one topic or sub-theme in the same evaluation and, consequently, increase its importance in the total sequence. If the weighted average did not exist, teachers would have two possible paths:

* perform many more exams, so that each of them had the same importance (the same weight) as the rest and it was possible to calculate the grade point average using the traditional method;

* unfairly or inconsistently assess student performance, giving equal weight to exams which have very different degrees of demand.

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