1. What is Weighted Mean?

The weighted mean is a type of average where some data points contribute more than others to the final average. It's calculated by multiplying each value by its weight, summing these products, and then dividing by the sum of the weights.

2. How Does the Calculator Work?

The calculator uses the weighted mean formula:

Where:

• \( value \) — Individual data values
• \( weight \) — Corresponding weights for each value
• \( \sum \) — Summation symbol

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

3. Importance of Weighted Mean

Details: Weighted mean is crucial in statistics when different data points have different levels of importance or reliability. It's used in grade calculations, financial analysis, survey analysis, and many other fields where not all observations contribute equally to the average.

4. Using the Calculator

Tips: Enter values and weights as comma-separated lists. Both lists must have the same number of elements. Weights should be positive numbers, and the sum of weights cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: When should I use weighted mean instead of regular mean?
A: Use weighted mean when some data points are more important or reliable than others, or when they represent different proportions of the whole.

Q2: Can weights be negative?
A: Typically, weights should be positive numbers. Negative weights would invert the contribution of values, which is usually not meaningful in most applications.

Q3: What happens if the sum of weights is zero?
A: The weighted mean is undefined when the sum of weights is zero, as division by zero is mathematically impossible.

Q4: How are weights determined?
A: Weights are determined based on the relative importance, reliability, or frequency of each value. The specific method depends on the application context.

Q5: Can I use decimal weights?
A: Yes, weights can be any positive real numbers, including decimals and fractions.