1. What is a Weighted Average?

Definition: A weighted average is an average where each value has a specific weight or importance assigned to it.

Purpose: It provides a more accurate measurement than a simple average when values have different levels of importance.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \mu \) — Weighted average
• \( w_i \) — Weight of the ith value
• \( x_i \) — The ith value
• \( n \) — Number of values

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 statistics, finance, education (GPA calculation), inventory management, and many other fields where not all values contribute equally.

4. Using the Calculator

Tips:

• Enter values separated by commas (e.g., 85,90,78)
• Enter corresponding weights separated by commas (e.g., 0.3,0.5,0.2)
• Number of values must equal number of weights
• Weights should typically sum to 1 (but not required)

5. Frequently Asked Questions (FAQ)

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

Q2: Can weights be negative?
A: Mathematically yes, but in most practical applications weights are positive numbers.

Q3: What if my weights don't sum to 1?
A: The calculator will still work correctly. The formula automatically normalizes the weights.

Q4: Where is weighted average used in real life?
A: Common uses include GPA calculation, stock market indices, survey analysis, and performance metrics.

Q5: What happens if I enter more values than weights?
A: The calculator will only process pairs where both value and weight exist.