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Weighted Average Formula

Weighted average is an average in which each quantity to be averaged is assigned a weight. These weightings determine the relative importance of each quantity on the average. Weightings are the equivalent of having that many like items with the same value involved in the average.

Weightings are equivalent of having many similar items with the same value involved in the average. For instance, let x be the observations and w be the weights of the observations, the formula of weighted average is given below.

\[\large \overline{x}=\frac{\sum_{i=1}^{n}w_{i}x_{i}}{\sum_{i=1}^{n}w_{i}}\]

Or in simple terms we can write the formula as below

\[\large Weighted\;Average=\frac{Sum\;of\;Weighted\;Terms}{Total\;Number\;of\;Terms}\]

To find the weighted term, multiply each term by its weighting factor, which is the number of times each term occurs.

Solved Examples

Example: A class of 25 students took a science test. 10 students had an average score of 80. The other students had an average score of 60. What is the average score of the whole class?

Solution:

Step 1: To get the sum of weighted terms, multiply each average by the number of students that had that average and then sum them up.

80 × 10 + 60 × 15 = 800 + 900 = 1700

Step 2: Total number of terms = Total number of students = 25

Step 3: Using the formula

$Weighted\;Average=\frac{Sum\;of\;Weighted\;Terms}{Total\;Number\;of\;Terms}$
$=\frac{1700}{25}$
=68

Answer: The average score of the whole class is 68.

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