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, 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:

• \( x_i \) — 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 (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. 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 simple average?
A: Simple average treats all values equally, while 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 if the sum of weights equals zero?
A: The calculation becomes undefined (division by zero), which is mathematically invalid. Weights should be chosen so their sum is positive.

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

Q5: Can I use percentages as weights?
A: Yes, percentages work well as weights. If weights sum to 100%, the calculation simplifies as the denominator becomes 1.