1. What is Weighted Mean?

The weighted mean (or weighted average) is a type of average where each value has a specific weight that contributes to the final result. Unlike the regular arithmetic mean where all values are equally weighted, the weighted mean gives more importance to some values than others.

2. How Does the Calculator Work?

The calculator uses the weighted mean formula:

Where:

• \( WM \) — Weighted mean
• \( w_i \) — Weight of the i-th element
• \( x_i \) — Value of the i-th element
• \( n \) — Number of elements

Explanation: Each value is multiplied by its weight, these products are summed, and then divided by the sum of the weights.

3. Applications of Weighted Mean

Details: Weighted means are used in grade calculations, stock indices, survey analysis, and anywhere where some values should contribute more to the average than others.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between mean and weighted mean?
A: Regular mean treats all values equally, while weighted mean assigns different importance (weights) to each value.

Q2: Can weights be zero or negative?
A: Typically weights should be positive numbers. Zero weight means the value doesn't contribute, and negative weights can lead to counterintuitive results.

Q3: What if the sum of weights is zero?
A: The weighted mean is undefined in this case as it would require division by zero.

Q4: How is weighted mean used in education?
A: Different assignments (tests, homework) can have different weights when calculating final grades.

Q5: What's an example of weighted mean in finance?
A: Stock market indices like the S&P 500 use weighted averages where larger companies have greater influence on the index value.