1. What is a Weighted Average Calculator?

Definition: This calculator computes the weighted average of values where some values contribute more significantly than others based on assigned weights.

Purpose: It helps in statistical analysis, grading systems, financial calculations, and any scenario where different data points have different levels of importance.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \mu \) — Weighted average
• \( w_i \) — Weight of the i-th value
• \( x_i \) — The i-th value

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

3. Importance of Weighted Average

Details: Weighted averages provide more accurate results than simple averages when dealing with data points of varying importance or reliability.

4. Using the Calculator

Tips:

• Add multiple value-weight pairs using the "Add Row" button
• Remove rows with the "Remove Row" button
• Weights must be ≥ 0 (typically > 0)
• At least one pair must be entered

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between average and weighted average?
A: Regular average treats all values equally, while weighted average accounts for varying importance or frequency of values.

Q2: Can weights be zero?
A: Technically yes, but values with zero weights don't contribute to the result. Negative weights are not allowed.

Q3: What are common applications of weighted averages?
A: Grade calculations, stock indices, survey analysis, and any situation where some data points are more significant than others.

Q4: What happens if all weights are equal?
A: The weighted average becomes identical to the regular arithmetic mean.

Q5: How many value-weight pairs can I enter?
A: You can add as many as needed, though practical limits depend on your browser's memory.