Weighted average is a powerful concept in mathematics and statistics that allows you to find the proportional mean of a set of numbers. Whether you’re a student solving math problems or a professional dealing with statistical data, understanding how to calculate a weighted average is essential. In this guide, we will break down the process step-by-step.

What is a Weighted Average?

A weighted average is a mathematical calculation that takes into account the importance, significance, or weight of each number in a given dataset. Unlike a regular average, where each number has the same weight, a weighted average assigns different weights or proportions to each number.

When and Why is a Weighted Average Used?

A weighted average is used when you want to give more importance or influence to certain numbers over others in the calculation. This is often the case when dealing with data that has different levels of significance or when analyzing data from different sources.

A weighted average is commonly used in various fields, including finance, economics, education, and market research. For example, in finance, stock market indices are often calculated using a weighted average of the stock prices of individual companies.

How to Calculate a Weighted Average

Calculating a weighted average involves a straightforward step-by-step process:

  1. Assign weights to each number: Start by assigning a weight to each number in the dataset. The weights should reflect the relative importance of each number. For example, if you are calculating a weighted average based on test scores, you could assign a weight of 2 to the scores of mid-term exams and a weight of 3 to the scores of final exams.
  2. Multiply each number by its weight: Multiply each number in the dataset by its corresponding weight. This will give you weighted values for each number.
  3. Sum the weighted values: Add up all the weighted values to get the total sum.
  4. Sum the weights: Add up all the weights assigned to each number.
  5. Divide the total sum by the total weight: Divide the total sum of the weighted values by the total weight to find the weighted average.

Example Calculation

Let’s walk through an example to help illustrate the process. Suppose you have a dataset of three numbers:

  • Number 1: 10 (Weight: 2)
  • Number 2: 15 (Weight: 3)
  • Number 3: 20 (Weight: 4)

Using the steps outlined above:

  1. Assign the weights: 2, 3, and 4 to numbers 1, 2, and 3 respectively.
  2. Multiply each number by its weight: 10 x 2 = 20, 15 x 3 = 45, 20 x 4 = 80.
  3. Sum the weighted values: 20 + 45 + 80 = 145.
  4. Sum the weights: 2 + 3 + 4 = 9.
  5. Divide the total sum by the total weight: 145 ÷ 9 ≈ 16.11.

Therefore, the weighted average of the dataset is approximately 16.11.

Calculating a weighted average allows you to find the proportional mean of a set of numbers, taking into account their individual weights. By following the step-by-step process outlined in this guide, you can confidently calculate the weighted average for any dataset. Remember, a weighted average is a versatile tool used in various fields, and understanding its concept is crucial for making sound decisions based on data analysis.

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