A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.

Weighted Average

Weighted average is considered the average where a weight is assigned to each of the quantities that are needed to be averaged. This weighting helps us in determining the respective importance of each quantity, on average. A weighted average can be considered to be more accurate than any simple average, as all the numbers in the set of data are assigned with identical weights. Let us explore the topic of weighted average, by understanding what is the meaning of weighted average, real-life examples, and solve a few examples using the formula.

1. What is the Meaning of Weighted Average?
2. Real-Life Examples on Weighted Average
3.. Weighted Average Formula
4.. FAQs on Weighted Average

What is the Meaning of Weighted Average?

Weight average also called weighted mean is helpful to make a decision when there are many factors to consider and evaluate. Each of the factors is assigned some weights based on their level of importance, and then the weighted average is calculated using a mathematical formula. The weighted average assigns certain weights to each of the individual quantities. The weights do not have any physical units and are only numbers expressed in percentages, decimals, or integers. The weighted average formula is the summation of the product of weights and quantities, divided by the summation of weights.

\(\text{Weighted Average} = \dfrac{\sum (\text {Weights} \times \text {Quantities})}{\sum \text {Weights}} \)

Definition of Weighted Average

When some quantities are more important than the others and do not contribute equally to the final result thus multiplying them to a coefficient is called weighted average. It is a simple process of deriving at an average value between two or quantities when weight is added to it. For example, a student realizes that the scores after an exam is two times more important than the scores acquired during the quiz. This is called the weighted average method.

Real-Life Examples on Weighted Average

A few real-life examples would help us better understand this concept of weighted average.

A teacher evaluates a student based on the test marks, project work, attendance, and class behavior. Further, the teacher assigns weights to each criterion, to make a final assessment of the performance of the student. The image below shows the weight of all the criteria that help the teacher in her assessment. The average of the weights helps in showing a clear picture.

Example of Weighted Average

A customer's decision to buy or not to buy a product depends on the quality of the product, knowledge of the product, cost of the product, and service by the franchise. Further, the customer assigns weight to each of these criteria and calculates the weighted average. This will help him in making the best decision while buying the product.

Example on Weighted Average

For appointing a person for a job, the interviewer looks at his personality, working capabilities, educational qualification, and team working skills. Based on the job profile, these criteria are given different levels of importance(weights) and then the final selection is done.

Example on Weighted Average

Weighted Average Formula

The weighted average formula is more descriptive and expressive in comparison to the simple average as here in the weighted average, the final average number obtained reflects the importance of each observation involved. In the weighted average, some data points in the data set contribute more importance to the average value, unlike in the arithmetic mean. It can be expressed as:

Weighted Average = Sum of weighted terms/Total number of terms

Weighted Average Formula

Let us look at an example to understand this better.

Example: The below table presents the weights of different decision features of an automobile. With the help of this information, we need to calculate the weighted average.

Quantity Weight
Safety - 8/10 40%
Comfort - 6/10 20%
Fuel mileage - 5/10 30%
Exterior looks - 8/10 10%

Solution: Let us now calculate the final rating of the automobile using the concept of weighted average.

\[ \begin{align} \text{Weighted Average} &= 40\%\times \frac{8}{10} + 20\% \times \frac{6}{10} + 30\% \times \frac{5}{10} + 10\% \times \frac{8}{10} \\ &= 0.4\times 0.8 + 0.2 \times 0.6 + 0.3 \times 0.5 + 0.1 \times 0.8 \\ &= 0.32+0.12 + 0.15 + 0.08 \\ &= 0.67 = 6.7/10 \end{align} \]

The overall rating of the car is 6.7/10.

☛Important Notes

  1. The weights given to the quantities can be decimals, whole numbers, fractions, or percentages.
  2. If the weights are given in percentage, then the sum of the percentage should be 100%.
  3. Weighted average for quantities (x)i having weights in percentage (P)i% is:
    Weighted Average = ∑ (P)i% × (x)i

☛Related Topics on Trapezoid

Listed below are a few topics that are related to a weighted average.

 

Weighted Average Examples

  1. Example 1: Sid wants to purchase a mobile phone and checks on the internet and finds the rating of 8/10 for features and 7/10 for durability. Based on his requirement Sid gives a weightage of 60% to features and 40% for durability. How can you help Sid calculate the final rating for the mobile phone?

    Solution:

    The final rating of the mobile phone can be calculated using the concept of weighted average.

    Rating for features = 8/10 and rating for durability = 7/10

    Weight for features = 60% and weight for durability = 40%

    \[\begin{align} \text{Weighted Average} &= 60\% \times \frac{8}{10} + 40\% \times \frac{7}{10} \\ &= 0.6 \times 0.8 + 0.4 \times 0.7 \\ &= 0.48 + 0.28 \\ &= 0.76 \\ &= \frac{7.6}{10} \end{align} \]

    Therefore, the final rating of the mobile is 7.6/10.

  2. Example 2: In a 50 over cricket match, the average runs scored by a team for different sessions of the innings are given below. Find the average runs scored by the team in that innings.

    First ten overs - 8 runs per over
    10 to 35 overs – 5 runs per over
    Last 15 overs – 9 runs per over

    Solution:

    To find: Average runs scored.
    Given: Total overs = 50
    \(w_1\) = 8
    \(w_2\) = 5
    \(w_3\) = 9
    \(x_1\) = 10
    \(x_2\) = 25
    \(x_3\) = 15
    Now, to find the sum of weighted terms, multiply the average runs scored in the respective session and then add them up.
    Sum of weighted terms = \(w_1\) ×\(x_1\) +\(w_2\)× \(x_2\) +\(w_3\)× \(x_3\) = 8(10) + 5(25) + 9(15) = 80 + 125 + 135 = 340
    Now, using the weighted average formula,
    Weighted Average = Sum of weighted terms/Total number of terms
    = 340/50
    = 6.8

    Therefore, the average runs scored in that innings by the team = 6.8.

  3. Example 3: Ron has a supermarket and he earns a profit of $5000 from his groceries, $2000 from vegetables and $1000 from dairy products. He wants to predict his profit for the next month. He assigns weights of 6 to groceries, 5 to vegetables, and 8 to dairy products. Can you help Ron on how to calculate weighted average of his profits?

    Solution:

    Let us first present the profits and the weightage in a table.

    Profits Weights
    Groceries - $5000 6
    Vegetables - $2000 5
    Diary Products - $1000 8

    Further applying the formula of weighted average to the above data, we have:

    \[\begin{align} \text{Weighted Average} &= \frac{6 \times 5000 + 4 \times 2000 + 8 \times 2000}{6 + 4 + 8} \\ &= \frac{30000 + 8000 + 16000}{18} \\ &=\frac{54000}{18} \\ &= 3000\end{align} \]

    Therefore, the weighted average of the profits is $3000.

View Answer >

go to slidego to slidego to slide

Have questions on basic mathematical concepts?
Become a problem-solving champ using logic, not rules. Learn the why behind math with our certified experts

Book a Free Trial Class

FAQs on Weighted Average

What is Weighted Average?

The weighted average is the method of calculating the average, in which each of the quantities is assigned a weight. Different weights are assigned to each of the quantities, based on their level of importance. Weighted average is the summation of the product of the weights and quantities, divided by the summation of the weights.

How to Calculate Weighted Average?

We use the following weighted average formula for calculation.

\[ \overline x = \frac{w_1x_1 + w_2x_2 + ......+ w_nx_n}{w_1 + w_2 + ... + w_n} \]

Here \(w_1, w_2, w_3, ...... w_n\) are the weights and \(x_1, x_2, x_3, ....... x_n\) are the quantities.

What is Weighted Average Cost of Capital?

The weighted average cost of capital helps to find the capital value of the company. The capital includes fixed assets, cash in hand, goods, brand value. All of these are assigned certain weights and the weighted average formula is used to calculate the weighted average cost of capital.

How to Calculate Weighted Average Using Weighted Average Formula?

To calculate the weighted average we need to follow the following steps given below:

  • Observe the weight of individual items given in the problem
  • Determine the individual weight of data or items given.
  • Multiply the weight individually by each value and add the results together
  • Now apply the weighted average formula that is (Sum of weighted terms/Total number of terms).

How To Calculate the Sum of Weighted Terms Using the Weighted Average Formula?

If the weighted average of items is known along with a total number of terms then we can easily calculate the weighted average by:

  • Determining the individual weight of items given.
  • Multiplying the weight individually by each value and sum up the results together

What Is the Use of Weighted Average Formula?

The weighted average formula is used to calculate the mean weighted value of the data with n terms. It is described as (Sum of weighted terms/Total number of terms).

Download FREE Study Materials
Weighted Average Worksheets
Math worksheets and
visual curriculum