Question

Design an algorithm to find the weighted average of four test scores. The four test scores and their respective weights are given in the following format: testscore1 weightTestscore1 For example, sample data is as follows: 750.20 950.35 850.15 650.30

Short answer

The weighted average of the test scores is 805.

Step-by-step solution

Understanding the Data Format

The data format provided consists of pairs of test scores and their corresponding weights. For example, "750.20" represents a test score of 750 with a weight of 0.20. Similarly, we have "950.35" for a test score of 950 with a weight of 0.35, "850.15" for a score of 850 with a weight of 0.15, and "650.30" for a score of 650 with a weight of 0.30.

Calculate the Weighted Score for Each Pair

To find the weighted score for each test score, multiply the test score by its weight. For "750.20", the calculation is: \( 750 \times 0.20 = 150 \). Repeat this for the other pairs: - \( 950 \times 0.35 = 332.5 \) - \( 850 \times 0.15 = 127.5 \) - \( 650 \times 0.30 = 195 \).

Compute the Total Weighted Score

Add all the weighted scores from Step 2 to get the total weighted score. Therefore, \( 150 + 332.5 + 127.5 + 195 = 805 \).

Calculate the Sum of Weights

Add all the weights of the test scores together to find the total weight. Thus, \( 0.20 + 0.35 + 0.15 + 0.30 = 1.00 \).

Compute the Weighted Average

The weighted average is calculated by dividing the total weighted score by the total weight. Thus, \( \frac{805}{1.00} = 805 \).

Conclusion

The weighted average of the test scores, with the given weights, is 805.

Key concepts

Weighted Average

The concept of a weighted average might sound complex, but it's actually quite approachable with an example. A weighted average is used when different items in the dataset contribute unequally to the final result. In this exercise, each test score has a weight that indicates its importance. To compute a weighted average, you first multiply each item by its weight, then sum these products, and finally, divide by the sum of the weights. This allows us to consider both the values of the data and their relative significance. For instance, in our exercise, the test scores are 750, 950, 850, and 650, with associated weights of 0.20, 0.35, 0.15, and 0.30, respectively. This means that the test score of 950 has a higher influence on the weighted average because it has a greater weight. A weighted average is useful in many real-world scenarios, such as grades in courses where different activities have different impacts on the final grade, or in finance for portfolio management.

Test Scores

Test scores are quantitative measures of performance in assessments. In this exercise, four test scores are evaluated: 750, 950, 850, and 650. Test scores alone provide an indication of performance, but they don't account for the varying importance of each test. This is where weights come into play. By assigning weights to each test score, we can reflect their importance or contribution to the overall result. For example, a final exam might carry more weight than a midterm exam or a quiz. Thus, when computing an average or an overall score, it's crucial to account for these weights to get an accurate reflection of performance.

Step-by-Step Solutions

Step-by-step solutions are incredibly helpful for breaking down complex problems into manageable parts. By addressing one part at a time, it makes the overall problem less intimidating and easier to understand. This approach is not only good for solving math problems but is also beneficial in algorithm design and programming. In this exercise, the solution is divided into several steps:

• Understanding the data format
• Calculating the weighted scores for each test
• Computing the total weighted score and the sum of weights
• Determining the weighted average

Each step builds upon the previous one, ensuring that by the end, the complete solution is clear and logical. This method also mirrors how algorithms are developed: by identifying individual components, solving each one carefully, and then combining them into a full solution.

Programming Concepts

Algorithm design and programming concepts often overlap and enrich each other. In this exercise, the task of calculating a weighted average can be approached programmatically by automating the repeated tasks of multiplication and addition. Key programming concepts relevant here include:

• Data structures to store scores and weights
• Loops to iterate over scores and weights
• Arithmetic operations for calculations
• Functions for organizing code into reusable blocks

Essentially, algorithm design involves creating a clear path or set of steps to solve a problem. In this case, you create a loop that processes each score and its weight, multiplies them, and accumulates the results to find the weighted average. Programming teaches precision, allowing you to translate a logical set of steps, like those outlined here, into a script that consistently computes the answer regardless of how data changes.