1. What is Weighted Average?

A weighted average is an average where some data points contribute more than others to the final result. Each value is multiplied by a predetermined weight before summing, then divided by the sum of all weights.

2. How Does the Calculator Work?

The calculator uses the weighted average formula:

Where:

• \( WA \) — Weighted Average
• \( x_i \) — Individual values
• \( w_i \) — Corresponding weights (unitless)
• \( \sum \) — Summation of all terms

Explanation: The formula calculates the average where each value's contribution is proportional to its assigned weight.

3. Importance of Weighted Average

Details: Weighted averages are crucial in statistics, finance, education (GPA calculation), inventory management, and any situation where different data points have varying levels of importance.

4. Using the Calculator

Tips: Enter values and corresponding weights as comma-separated lists. Both lists must have the same number of elements. Weights should be positive numbers (sum cannot be zero).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between weighted average and regular average?
A: Regular average gives equal importance to all values, while weighted average allows different values to contribute differently based on their weights.

Q2: Can weights be negative?
A: While mathematically possible, negative weights are generally not used in practical applications as they can produce counterintuitive results.

Q3: What happens if the sum of weights is zero?
A: The calculation becomes undefined (division by zero). Weights must sum to a non-zero value.

Q4: How are weights determined?
A: Weights are typically based on importance, frequency, reliability, or other relevant factors specific to the application.

Q5: Can I use decimal weights?
A: Yes, weights can be any real numbers (except zero when summing to zero). Decimal weights are commonly used in many applications.