Weighted Average Calculator

Weighted Average Formula:

\[ \text{Weighted Average} = \frac{\sum (Value_i \times Weight_i)}{\sum Weights} \]

Value 1:

unit

Weight 1:

proportion

Value 2:

unit

Weight 2:

proportion

Value 3:

unit

Weight 3:

proportion

Weighted Average:

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1. What is Weighted Average?

A weighted average is a type of mean where some data points contribute more significantly than others to the final average. Unlike a simple arithmetic mean, weighted averages account for the relative importance or frequency of each value in the dataset.

2. How Does the Calculator Work?

The calculator uses the weighted average formula:

\[ \text{Weighted Average} = \frac{\sum (Value_i \times Weight_i)}{\sum Weights} \]

Where:

\( Value_i \) — Individual values in the dataset (unit)
\( Weight_i \) — Corresponding weights for each value (proportion)
\( \sum \) — Summation of all terms

Explanation: Each value is multiplied by its corresponding weight, these products are summed, and then divided by the sum of all weights to get the weighted average.

3. Importance of Weighted Average

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

4. Using the Calculator

Tips: Enter three value-weight pairs. Values can be any real number, while weights must be non-negative numbers. The sum of weights should be greater than zero for meaningful results.

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 values with higher weights, reflecting their relative significance.

Q2: Can weights be percentages?
A: Yes, weights can be percentages, frequencies, or any proportional measure. The calculator normalizes them automatically.

Q3: What happens if all weights are equal?
A: If all weights are equal, the weighted average becomes identical to the simple arithmetic mean.

Q4: Are there limitations to weighted averages?
A: The accuracy depends on appropriate weight assignment. Incorrect weights can lead to misleading results. Also, weights must be non-negative.

Q5: Where is weighted average commonly used?
A: Common applications include GPA calculation, stock index computation, course grading, financial analysis, and survey data analysis.