Welcome! Today we'll explore weighted averages. A weighted average is an average where some values contribute more than others. Unlike a simple average where all values are treated equally, in a weighted average, each value is multiplied by its corresponding weight. This gives more importance to certain values based on their weights.
Now let's see how to calculate a weighted average step by step. First, multiply each value by its corresponding weight. Then, add all the weighted values together. Next, add all the weights. Finally, divide the sum of weighted values by the sum of weights to get your weighted average.
Let's visualize this with a bar chart. Each bar's height represents the value, while its width represents the weight. Notice how the middle bar is widest because it has the highest weight of 3. The weighted average line shows the result at 83.33, which is closer to the higher-weighted values.
Weighted averages have many real-world applications. In education, final grades often use weighted averages where exams count more than homework. In finance, stock market indices use market capitalization as weights. Survey data uses population weights, and quality control uses importance factors. These applications show why understanding weighted averages is essential in many fields.
To summarize, weighted averages assign different levels of importance to values based on their weights. The formula is the sum of weight times value, divided by the sum of weights. This method is more accurate than simple averages when dealing with data of varying importance. Weighted averages are essential tools in education, finance, research, and many other fields. Thank you for learning about weighted averages!