1. What is Weighted Average?

A weighted average is a type of average where each value in the dataset is assigned a specific weight that determines its relative importance. Unlike a simple average where all values are treated equally, weighted averages account for varying significance of different data points.

2. How Does the Calculator Work?

The calculator uses the weighted average formula:

Where:

• \( WA \) — 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 corresponding weight, these products are summed, and then divided by the sum of all weights.

3. Importance of Weighted Average

Details: Weighted averages are essential in statistics, finance, education (GPA calculation), inventory management, and any situation where different data points have different levels of importance.

4. Using the Calculator

Tips: Enter values and their corresponding weights as comma-separated lists. Both lists must have the same number of elements. Weights should be positive numbers.

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 assigns different importance (weights) to each value.

Q2: Can weights be zero or negative?
A: Weights should generally be positive numbers. Zero weights would make those values irrelevant, and negative weights could produce misleading results.

Q3: What are common applications of weighted averages?
A: Common uses include calculating GPA (course credits as weights), stock indices (market cap as weights), and survey analysis (respondent importance as weights).

Q4: How do I choose appropriate weights?
A: Weights should reflect the relative importance of each value in your specific context. This often requires domain knowledge.

Q5: What if the sum of weights equals zero?
A: The calculation becomes undefined (division by zero). Ensure at least one weight is positive.