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The concept of weighted average is a fundamental statistical tool used to find an average that reflects varying degrees of importance among quantities. Unlike an ordinary average where each number contributes equally, a weighted average assigns different weights to each value. This means some numbers count more towards the final average based on their assigned weight. This statistic is particularly useful in fields ranging from finance to sociology, where not all data points carry the same significance. For instance, in a student's grade point average, courses that are worth more credits have a higher impact than those worth fewer credits. The formula for the weighted average is:\[ \text{Weighted Average} = \frac{\sum (x_i \cdot w_i)}{\sum w_i} \]Where:

• \( x_i \) represents each value in the dataset.
• \( w_i \) is the respective weight of each value.

Understanding this concept is essential for data analysis and making informed decisions based on various values with different levels of importance.

Data analysis involves interpreting complex data to draw meaningful insights, and using a weighted average is a common technique in this process. When analyzing data, one significant aspect is understanding variance within the dataset—how different parts of the data influence the outcomes. In our exercise, weighing individual numbers helps clarify their relative importance and gives a clearer overall picture compared to using a simple mean that assumes equal weight. ### Applying Data Analysis with Weights In practical scenarios:

• Companies use weighted averages to calculate average production costs where different materials contribute unequally to the total.
• Weighted averages can adjust scores in assessments to give more significance to important tests or assignments.

By applying the weighted average, we can highlight crucial data points and ensure analysis reflects real-world scenarios more accurately, making decision-making more precise.

Mathematical computation ensures the accurate and reliable application of formulas like the weighted average. The formula \( \frac{\sum (x_i \cdot w_i)}{\sum w_i} \) might look complex initially, but breaking it down simplifies calculation. ### Step-by-Step Computational Process1. **Multiply Each Value by Its Weight:** - For the given values, execute: - \(10 \times 2 = 20\) - \(20 \times 3 = 60\) - \(30 \times 5 = 150\) 2. **Sum the Products** - Add the results of the products: \(20 + 60 + 150 = 230\) 3. **Sum the Weights** - Calculate the total of all weights: \(2 + 3 + 5 = 10\) 4. **Calculate the Weighted Average** - Divide the total product sum by the total weight sum: \( \frac{230}{10} = 23 \) Performing these computations accurately is vital for ensuring the calculated weighted average reflects the intended weighting of each value, crucial for precise statistical analysis and decision-making based on data.