1. What is Weighted Average?

A weighted average is an average where some data points contribute more than others to the final result. Unlike a simple average where all values are treated equally, weighted averages assign different weights to different values based on their importance or relevance.

2. How Does the Calculator Work?

The calculator uses the weighted average formula:

Where:

• \( WA \) — Weighted Average
• \( x_i \) — Individual values
• \( w_i \) — Weights assigned to each value
• \( \sum \) — Summation symbol

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 are crucial in many fields including education (calculating GPA), finance (portfolio returns), statistics, and research where different data points have varying levels of importance.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between simple average and weighted average?
A: Simple average treats all values equally, while weighted average assigns different importance (weights) to different values.

Q2: Can weights be negative?
A: Typically no, weights should be positive values. Negative weights would invert the contribution of values, which is not standard in weighted average calculations.

Q3: What if the sum of weights equals zero?
A: The calculation becomes undefined (division by zero). Ensure at least one weight is a positive number.

Q4: How are weights determined?
A: Weights are typically based on the relative importance, frequency, or relevance of each value in the specific context of the calculation.

Q5: Can I use decimal weights?
A: Yes, weights can be any positive numbers including decimals. The calculator will handle them appropriately.