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:

• \( \text{value} \) — Individual data values
• \( \text{weight} \) — Weight assigned to each value
• \( \sum \) — Summation of all elements

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 (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 both lists have the same number of elements. Weights should be positive numbers, and the sum of weights must be greater than 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 are some common applications of weighted averages?
A: Grade point averages (GPA), stock index calculations, customer satisfaction scores, and economic indicators often use weighted averages.

Q4: How should I choose appropriate weights?
A: Weights should reflect the relative importance, frequency, or reliability of each data point in your specific context.

Q5: What happens if the sum of weights is zero?
A: The calculation becomes undefined (division by zero), so weights must be chosen such that their sum is not zero.