Understanding Weighted-Average

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The weighted average is a fundamental concept in statistics and data analysis. It extends the traditional notion of the average (or mean) by incorporating weights that reflect the relative significance of individual data points. This versatility makes weighted averages a cornerstone technique in various domains, including machine learning, finance, and engineering.

In this story, we will try to understand the basics of weighted-average and how important it is in some applications.

Weighted Averages

In a standard average, all data points contribute equally to the final result. In contrast, a weighted average assigns a specific weight to each data point, signifying its importance in determining the overall average. These weights are typically non-negative numbers, with larger weights indicating a greater influence on the final outcome.

Mathematically, a weighted average can be represented as follows:

Weighted Average = Σ (wi * xi) / Σ wi

where:

• Σ (sigma) denotes summation.
• wi represents the weight assigned to the ith data point (xi).
• xi represents the value of the ith data point.