1. What is Weighted Average?

A weighted average is an average where some data points contribute more than others. Unlike a simple average where all values are treated equally, a weighted average assigns different weights to different values based on their importance or frequency.

2. How Does the Calculator Work?

The calculator uses the weighted average formula:

Where:

• \( Value_i \) — Individual values to be averaged
• \( Weight_i \) — Weight assigned to each value
• \( \sum \) — Summation of all elements

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), statistics, and research where different data points have different levels of importance.

4. Using the Calculator

Tips: Enter values and corresponding weights as comma-separated lists. Ensure you have the same number of values and weights. Weights should be positive numbers, and the sum of weights should not be zero.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between average and weighted average?
A: A simple average treats all values equally, while a weighted average gives more importance to some values based on their assigned 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 happens if the sum of weights is zero?
A: Division by zero is undefined, so the weighted average cannot be calculated if the sum of weights equals zero.

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

Q5: Can I use percentages as weights?
A: Yes, percentages can be used as weights. The calculator will work correctly as long as the weights are consistent (all using the same unit or scale).