Weighted Mean Calculator

What is a Weighted Mean?

A weighted mean is an average that takes into account the relative importance or weight of each value in a dataset. It's particularly useful when some values are more significant than others.

Formula and Its Meaning

The formula for weighted mean is:

\[\bar{x}_w = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}\]

Where:

• \(\bar{x}_w\) is the weighted mean
• \(x_i\) are the individual values
• \(w_i\) are the corresponding weights
• \(n\) is the number of values

Calculation Steps

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

Example Calculation

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

Values (X): 1, 2, 3, 4, 5

Weights: 5, 20, 40, 80, 100

1. Multiply values by weights: 1×5, 2×20, 3×40, 4×80, 5×100
2. Sum of products: 5 + 40 + 120 + 320 + 500 = 985
3. Sum of weights: 5 + 20 + 40 + 80 + 100 = 245
4. Weighted mean: 985 ÷ 245 = 4.02

Visual Representation

This scatter plot represents the example dataset. The size of each point represents its weight, and the red dashed line indicates the weighted mean (approximately 4.02).