1. What is Weighted Average?

A weighted average is an average where some values contribute more than others. Each value is multiplied by a weight before summing, and the total is divided by the sum of all weights. This gives more importance to values with higher weights.

2. How Does the Calculator Work?

The calculator uses the weighted average formula:

Where:

• \( \text{value} \) — Individual data points
• \( \text{weight} \) — Relative importance of each value
• \( \sum \) — Summation of all elements

Explanation: The formula calculates the mean where each value is scaled by its corresponding weight before averaging.

3. Importance of Weighted Average

Details: Weighted averages are crucial in statistics, finance, education (GPA calculation), and many scientific fields where not all observations have equal importance or reliability.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

Q2: Can weights be negative?
A: While mathematically possible, negative weights are rarely used in practical applications as they can produce counterintuitive results.

Q3: What are some common applications of weighted averages?
A: GPA calculation, stock index computation, survey analysis, and any situation where some data points are more significant than others.

Q4: What happens if the sum of weights is zero?
A: The calculation becomes undefined (division by zero), which is mathematically invalid.

Q5: How should I choose appropriate weights?
A: Weights should reflect the relative importance, reliability, or frequency of each value in your specific context.