Weighted Mean Formula
The weighted mean formula helps to find the mean of the quantities by assigning weights to the quantities. Based on the level of importance of the quantities, weights are assigned to the quantities. The weighted mean formula is the summation of the product of the weights and quantities, divided with the sum of the weights. The concept of the weighted mean is quite often used in accounts, to give different weights based on time or based on priority.
What is Weighted Mean Formula?
The below formula for weighted mean includes variables \(x_1\), \(x_2\), \(x_3\)...\(x_n\), and their weights \(w_1\), \(w_2\), \(w_3\)...\(w_n\) respectively. Here this is similar to the average and the weighted mean represents the summary value of all the available quantities. The weighted mean has the same units as that of the individual quantities.
\[ \bar x = \frac{w_1x_1 + w_2x_2 + ......+ w_nx_n}{w_1 + w_2 + ... + w_n} \]
\[\bar x = \frac{\sum w_nx_n}{\sum w_n} \]
Let us try out a few examples to better understand, how to use the weighted mean formula.
Solved Examples on Weighted Mean Formula

Example 1: A teacher provides the following weightage of 20% for class attendance, 30% for project work, 40% for tests, and 10% for home assignments. A student scores 80/100 for class attendance, 4/5 in project work, 35/50 in tests, and 8/10 in home assignments. Find the final score of the student.
Solution:
\(\begin{align} \bar x &= \frac{w_1x_1 + w_2x_2 + ......+ w_nx_n}{w_1 + w_2 + ... + w_n}
\\&=\frac{20\%.\frac{80}{100} + 30\%.\frac{4}{5} + 40\%.\frac{35}{50} + 10\%.\frac{8}{10}}{20\% + 30\% + 40\% + 10\%} \\&=\frac{20\%.0.8 + 30\%.0.8 + 40\%.0.7 + 10\%.0.8}{100\%} \\&=\frac{0.2 \times 0.8 + 0.3 \times 0.8 + 0.4 \times 0.7 + 0.1 \times 0.8}{1} \\&=0.16 + 0.24 + 0.28 + 0.08 \\&=0.76 \end{align} \)
Answer: Therefore, the final score of the student is 0.76. 
Example 2: For a job application 0.8 weightage is given to academic qualification, 0.7 is given to personality, 0.4 is given to the location. The prospective candidate scores 4.5/5 for academic qualification, 3/5 for personality, and 2.8/5 for location. Find the final score received by the candidate.
Solution:
\(\begin{align} \bar x &= \frac{w_1x_1 + w_2x_2 + ......+ w_nx_n}{w_1 + w_2 + ... + w_n}
\\&=\frac{0.8 \times \frac{4.5}{5}+ 0.7 \times \frac{3}{5} + 0.4 \times \frac{2.8}{5}}{0.8 + 0.7 + 0.4} \\&=\frac{0.8 \times 0.9 + 0.7 \times 0.6 + 0.4 \times 0.56}{0.19} \\&=\frac{0.72 + 0.42 + 0.224}{0.19} \\&=\frac{1.364}{0.19} \\&= 7.18 \end{align} \)
Answer: Hence, the final score of the candidate is 7.18.