Weighted Average Calculator

Weighted Average Formula:

\[ \text{Weighted Average} = \frac{\sum (x_i \times w_i)}{\sum w_i} \]

Weighted Average:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Weighted Average?

A weighted average is a type of average where each value in the dataset is multiplied by a predetermined weight before the final calculation is made. This allows certain values to contribute more to the final average than others.

2. How Does the Calculator Work?

The calculator uses the weighted average formula:

\[ \text{Weighted Average} = \frac{\sum (x_i \times w_i)}{\sum w_i} \]

Where:

\( x_i \) — Individual values in the dataset
\( w_i \) — Weights corresponding to each value
\( \sum \) — Summation of all items

Explanation: Each value is multiplied by its weight, these products are summed, and then divided by the sum of all weights.

3. Importance of Weighted Average

Details: Weighted averages are crucial in many fields including education (GPA calculation), finance (portfolio returns), and statistics. They provide a more accurate representation when some values are more significant than others.

4. Using the Calculator

Tips: Enter values and corresponding weights separated by commas or new lines. The number of values must match the number of weights. Weights can be any positive number (they don't need to sum to 1).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between average and weighted average?
A: In a regular average, all values contribute equally. In a weighted average, some values contribute more based on their assigned weights.

Q2: Can weights be negative?
A: Typically no, weights should be positive numbers. Negative weights would invert the contribution of that value to the average.

Q3: What if my weights sum to 1?
A: If weights sum to 1, the weighted average formula simplifies to the sum of (value × weight) for all items.

Q4: How is this different from a moving average?
A: A moving average calculates averages over different subsets of data points, while weighted average applies different weights to all data points.

Q5: What are common applications of weighted averages?
A: Common applications include GPA calculation, stock index calculations, survey analysis, and any situation where some data points are more important than others.