In a weighted average, greater weight is attributed to a certain piece of information.
The figure that is identical or closest to the arithmetic mean is known as the average . The average can also be the point at which something divides in half.
The notion of weighted average is used to name a calculation method that is applied when, within a series of data, one of them has greater importance . There is, therefore, one piece of information with greater weight than the rest. The weighted average consists of establishing said weight, also known as weighting , and using said value to calculate the average.
Calculating the weighted average
With this clear, we can understand how the weighted average is calculated. First we must multiply each data by its weighting and then add these values. Finally we must divide this sum by the sum of all the weights.
The most common use of this calculation is linked to certain evaluations . Suppose that, to complete a certain course , a student must take five regular exams and a final exam that is equivalent to the other five exams. This means that, if each regular exam has a weight of 1 , the final exam will have a weight of 5 .
The student in question obtains the following grades: 6 , 7 , 5 , 7 and 8 in the regular exams and 6 in the final exam. Using the formula already mentioned, the weighted average of this student's grades will be equal to the sum of each one multiplied by their 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 weighted average is often used when evaluating students' knowledge.
A resource of great importance
The importance of the weighted average may not be obvious but, on the contrary, it is a very useful technique and can make a considerable difference to the calculation of the normal average. Returning to the example presented 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 piece of data were not taken into account : if we simply added the six grades and We 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 passing grade were the latter; In such a case, proceeding incorrectly to calculate the average (that is, ignoring the weight of each data and simply taking the average) would lead the student to think that they have passed the exam successfully, despite this not being true. If the last exam were longer and had a weight four times greater (20), the distance between both results would be truly considerable, since the weighted average would be 4.65.
The weighted average in educational evaluations
What advantage does the existence of the weighted average offer a teacher when preparing a series of evaluations? Would you be able to test your students on the same topics if you did not have this technique to calculate their grades? The main benefit consists of the possibility of grouping more than one topic or subtopic in the same evaluation and consequently increasing its importance in the total sequence. If the weighted average did not exist, teachers would have two possible paths:
* carry out 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 average of the grades using the traditional method;
* evaluate the performance of students in an unfair or inconsistent manner, giving the same weight to exams that present very different degrees of demand.