1. What is Weighted Average?

A weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set. Unlike a simple average where all numbers are treated equally, a weighted average assigns weights that determine the relative importance of each number.

2. How Does the Calculator Work?

The calculator uses the weighted average formula:

Where:

• \( WA \) — Weighted average
• \( w_i \) — Weight of the ith observation
• \( x_i \) — Value of the ith observation
• \( n \) — Number of observations

Explanation: Each value is multiplied by its weight, these products are summed, and then divided by the sum of the 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 their corresponding weights separated by commas. Both lists must be of equal length. Weights must be positive numbers (zero is allowed but will exclude that value from the calculation).

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 some values more "weight" or influence than others.

Q2: Can weights be zero?
A: Yes, but values with zero weight won't contribute to the calculation (equivalent to excluding them).

Q3: What if the sum of weights is zero?
A: The calculation is undefined (division by zero). You must have at least one non-zero weight.

Q4: How is this different from a moving average?
A: A moving average considers time sequence, while weighted average considers importance regardless of sequence.

Q5: Where is weighted average commonly used?
A: Common applications include GPA calculation, stock indices, survey analysis, and inventory valuation.