Weighted Average calculator

If all the numbers to be averaged have each equal importance in the set, we simply take the arithmetic mean of the numbers. Weighted average is a special type of mean when the numbers have unequal importance (or unequal weights). For example, when the grades of a student are calculated, it may happen that some assignments or exams are assigned greater weightage than the other. For instance, a final exam score has a greater weight than a quiz conducted in class. This is one of the most common examples of weighted average.

Given below are some important properties of weighted average.

Weight – This indicates the importance of each number in the set of numbers whose average is to be found.

Number – The entities in the data set which are assigned different weights according to their importance in the set.

Weighted average – The average of the numbers when each number is of unequal importance in the data set. In other words, some number contribute more (have greater importance) than the others (have lesser importance).

Arithmetic mean – When the entities to be averaged have equal weights, we simply sum up all the entities and divide that by the total number of entities.

The formula for weighted average is as follows. $$ Weighted \,average \, = \; {{w_1 x_1+w_2 x_2+w_3 x_3+⋯+w_n x_n}\over{w_1+w_2+w_3+⋯+w_n}} $$

Here, x₁,x₂,… x_n indicate the n numbers whose average is to be found and w₁,w₂,… w_n indicate the respective weights of these numbers.

To find the weighted average, we first multiply each number with its respective weight, and then divide that sum by the total number of weights.

Given below are some key characteristics of the weighted average.

Weighted average is used when some numbers to be averaged make unequal contributions to the data set (or have unequal importance) with respect to the others.

The numbers to be averaged may be integers or whole numbers. The weights are usually positive integers or positive real numbers.

The weighted average always lies between the maximum and minimum values of the set of numbers. If all the numbers being averaged are equal, the weighted average will be equal to that number itself.

If the value of each number being averaged is increased or decreased by the same amount, the same will be reflected in the weighted average.

If the value of each number being averaged is multiplied or divided by the same amount, the weighted average will also be multiplied or divided accordingly.

If the numbers being averaged have the same weights, this reduces to a case of arithmetic mean. In that case, we simply sum up the entities and divide by the total number of entities.

Some applications of the weighted average are:

For calculating the final grade of students when each examination or assignment contributes a different amount to the final, depending on their importance.

In manufacturing companies, the products made are sold at different costs depending on how valuable they are.

When the average performance of a sportsperson is evaluated, a weighted average is used because each type of performance is not equally significant. For example, to calculate the batting average for a baseball player, each hit carries a different weight.

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