Weighted Average Calculator

What is a Weighted Average?

A weighted average is a type of average where each quantity to be averaged is assigned a weight. These weightings determine the relative importance of each quantity on the average. Weighted averages are used when some data points are more important than others.

Formula and Its Meaning

The formula for weighted average is:

\[\text{Weighted Average} = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}\]

Where:

• \(w_i\) represents the weight for the \(i\)-th item
• \(x_i\) represents the value of the \(i\)-th item
• \(n\) is the total number of items

Calculation Steps

1. Multiply each value by its weight
2. Sum all these products
3. Divide by the sum of all weights

Example Calculation

Let's calculate the weighted average for the following data:

Value (\(x_i\))	Weight (\(w_i\))
85	0.2
90	0.3
92	0.5

Step 1: Multiply each value by its weight

• 85 × 0.2 = 17
• 90 × 0.3 = 27
• 92 × 0.5 = 46

Step 2: Sum all these products

17 + 27 + 46 = 90

Step 3: Sum all weights

0.2 + 0.3 + 0.5 = 1

Step 4: Divide the sum of products by the sum of weights

90 ÷ 1 = 90

Therefore, the weighted average is 90.

Visual Representation

This chart represents the example data. The size of each point corresponds to its weight, and the red dashed line indicates the weighted average.