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 frequency.

2. How Does The Calculator Work?

The calculator uses the weighted average formula:

Where:

• \( x_i \) — Individual values in the dataset
• \( w_i \) — Weights assigned to each value
• \( \sum \) — Summation symbol (add all values)

Explanation: Multiply each value by its weight, sum these products, then divide by the sum of all weights.

3. Applications Of Weighted Average

Details: Weighted averages are used in grade calculations, financial analysis (stock indices), survey analysis, quality control, and any situation where certain values should have more influence on the result than others.

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 representing the relative importance of each value.

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: Division by zero is undefined, so the calculator will return an error if the total weight sum is zero.

Q4: How are weights determined?
A: Weights are typically based on importance, frequency, reliability, or other contextual factors specific to your application.

Q5: Can I use percentages as weights?
A: Yes, percentage weights work well. The calculator normalizes weights automatically, so the relative proportions matter more than the absolute values.