# Weighted Average Formula

Before going to learn the weighted average formula, let us see what is a weighted average. It's an 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 study about weighted average formula using solved examples.

## What Is a 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

Let us see the applications of the weighted average formula in the following section.

## Examples Using Weighted Average Formula

Let us solve some interesting problems using the weighted average formula.

**Example 1: **In a class of 30 students, the average height of 16 students is 100 cm. The remaining students have an average height of 115 cm. What is the average height of the whole class?

**Solution: **

To find: Average height of students of the class.

Given: Total number of students = 30

\(w_1\) = 16

\(w_2\) = 30 - 16 = 14

\(x_1\) = 100

\(x_2\) = 115

Now, to find the sum of weighted terms, multiply the average height with the respective students and then add them up.

Sum of weighted terms = \(w_1\) ×\(x_1\) +\(w_2\)× \(x_2\) = 16(100) + 14(115) = 1600 + 1610 = 3210

Now, using the weighted average formula,

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

= 3210/30

= 107

**Answer: Average height of students of the class = 107**

**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

**Answer: Average runs scored in that innings by the team = 6.8**

**Example 3:** A machine shop owner purchases few items 2000 units of a product at $2 each, 1500 at $1 each, and 500 at $3 each. Using the units as the weight find the weighted average cost of items.

Solution: Using the weighted average formula,

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

Sum of weighted terms = \(w_1\) ×\(x_1\) +\(w_2\)× \(x_2\) +\(w_3\)× \(x_3\)

= $2(2000) + $1(1500) + $3(500) = ($4000 + $1500 + $1500) = $7000

Total number of terms = 2000 + 1500 + 500 = 4000

Weighted Average = 7000 / 4000 = $1.75

Hence the weighted average cost is $1.75 per unit.

## FAQs on Weighted Average Formula

### 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).