Mastering Weighted Averages: A Simple Approach for Students

What is the weighted average of the scores 75, 80, 88, and 93 with weights 1, 2, 3, and 4?

• A. 85.3
• B. 87.1
• C. 90.0
• D. 88.5

Answer: (B)

To find the weighted average of the scores with their respective weights, we first multiply each score by its corresponding weight and then sum these products. The scores and their weights are as follows: - Score 75 with weight 1: \( 75 \times 1 = 75 \) - Score 80 with weight 2: \( 80 \times 2 = 160 \) - Score 88 with weight 3: \( 88 \times 3 = 264 \) - Score 93 with weight 4: \( 93 \times 4 = 372 \) Next, we add these products together: \[ 75 + 160 + 264 + 372 = 871 \] Now, we also need to sum the weights: \[ 1 + 2 + 3 + 4 = 10 \] Finally, we calculate the weighted average by dividing the total sum of the products by the total sum of the weights: \[ \text{Weighted average} = \frac{871}{10} = 87.1 \] This is why the weighted average is 87.1, which corresponds to the size of the score distribution influenced by their different weights, providing a more accurate

Are you preparing for the Algebra Practice Test and feeling a bit overwhelmed by concepts like weighted averages? Trust me, you’re not alone! Many students scratch their heads at this topic, thinking, “How in the world do I make sense of these numbers?” Well, worry not! Let’s break it down together, shall we?