Weighted Average Calculator

Weighted Average Formula:

\[ WA = \frac{\sum (x_i \times w_i)}{\sum w_i} \]

Weighted Average (WA):

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1. What is Weighted Average?

A weighted average is an average where some data points contribute more than others to the final result. 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:

\[ WA = \frac{\sum (x_i \times w_i)}{\sum w_i} \]

Where:

\( x_i \) — Individual values in the dataset
\( w_i \) — Weights assigned to each value
\( \sum \) — Summation of all elements

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 crucial in statistics, finance, education (GPA calculation), inventory management, and many other fields where different data points have varying levels of importance or relevance.

4. Using the Calculator

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

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 lead to counterintuitive results.

Q3: How are weights determined?
A: Weights are typically based on the relative importance, frequency, or reliability of each data point in the specific context.

Q4: What if the sum of weights is zero?
A: The weighted average becomes undefined when the sum of weights is zero, as division by zero is mathematically impossible.

Q5: Where is weighted average commonly used?
A: Common applications include GPA calculation, stock index computation, cost accounting, and survey analysis where responses have different reliability.