https://file.aiquickdraw.com/mathbot/file/1727840527182mxo9h60g.jpg

The equation in the image contains summations and weights, suggesting a form similar to a weighted average or linear combination. Here's a transcription and explanation of the mathematical expressions from the image:

1. \( W = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i} \)

This is a weighted average formula, where:

- \( W \) is the weighted average.
- \( w_i \) represents the weights for each item.
- \( x_i \) represents the values for each item.
- \( n \) is the total number of items.
- The numerator, \( \sum_{i=1}^{n} w_i x_i \), represents the sum of the product of weights and values.
- The denominator, \( \sum_{i=1}^{n} w_i \), represents the sum of the weights.

2. \( \sum_{i=1}^{n} w_i = 1 \)

This indicates that the sum of all the weights \( w_i \) equals 1. This condition typically appears in probability or statistical contexts, ensuring that the weights are normalized.

### Breakdown:
- The equation calculates a weighted average \( W \) where each value \( x_i \) is multiplied by its corresponding weight \( w_i \).
- The sum of the weights equals 1, which ensures that the weighted average is normalized.

Would you like more details or further explanations?

Here are 5 related questions to deepen understanding:
1. What is the significance of a normalized sum of weights (i.e., when \( \sum w_i = 1 \))?
2. How does a weighted average differ from a simple average?
3. In what practical scenarios are weighted averages commonly used?
4. How does changing the weights \( w_i \) affect the overall weighted average?
5. What other methods can be used to combine values besides weighted averages?

**Tip:** When working with weighted averages, ensure the sum of the weights is 1, or else the result will need to be rescaled accordingly.

The image contains a formula that involves summations and weights, which appears to calculate a weighted average.

Explore how to calculate a weighted average using summation formulas. This guide explains the process step-by-step, ensuring a thorough understanding of how weights and values contribute to the final result. Suitable for high school students.

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