Math Problem Statement

What is the formula and explanation of the weighted mean calculation?

Solution

The formula shown in the image is:

Mp=(xi×wi)wiMp = \frac{\sum (x_i \times w_i)}{\sum w_i}

Explanation:

This formula represents the calculation of the weighted mean (or weighted average), where:

  • xix_i represents the individual values.
  • wiw_i represents the weights associated with each xix_i.
  • (xi×wi)\sum (x_i \times w_i) is the sum of the products of values and their respective weights.
  • wi\sum w_i is the sum of all weights.

The weighted mean MpMp gives more importance to some values based on their associated weights.

Would you like a detailed breakdown of this formula or an example? Here are some related questions you might find helpful:

  1. What is the significance of using a weighted mean versus a regular mean?
  2. How do you choose the weights wiw_i for each value xix_i?
  3. Can this formula be applied to non-numeric datasets?
  4. How does changing the weights affect the value of the weighted mean?
  5. What are some real-world applications of the weighted mean?

Tip: Weighted means are useful when different data points contribute unequally to the final average, like calculating the average grade with different assignment weights.

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Math Problem Analysis

Mathematical Concepts

Statistics
Weighted Mean
Averages

Formulas

Mp = (Σ(x_i × w_i)) / Σ(w_i)

Theorems

Weighted Mean Theorem

Suitable Grade Level

Grades 9-12