Question

In your economics class, each homework problem set is graded on the basis of a maximum score of 100 . You have completed 9 out of 10 of the problem sets for the term, and your current average grade is \(88 .\) What range of grades for your 10 th problem set will raise your overall average? What range will lower your overall average? Explain your answer.

Short answer

To raise the overall average, you need to score more than 88 on the 10th problem set. To lower the average, you need to score less than 88.

Step-by-step solution

Understanding the Problem

First, realize that the overall average is the total points obtained divided by the number of problem sets. To increase the average, the grade on the 10th set must be higher than the current average.

Calculating the Current Total Points

Calculate the total points earned so far by multiplying the current average by the number of sets completed: Total points = current average * number of sets = 88 * 9.

Determining Required Points for the 10th Set to Increase Average

To increase the average above 88, the score on the 10th set must be greater than 88.

Calculating the New Average if 10th Set Score is 100

Assume you get a perfect score on the 10th set. The new total points would be the current total plus 100. Divide this by 10 for the new average.

Determining Required Points for the 10th Set to Decrease Average

To decrease the average below 88, the score on the 10th set must be less than 88.

Key concepts

Economic Problem Solving

Understanding economic problem solving is essential for students studying microeconomics. This process involves identifying economic issues, gathering relevant information, and applying economic theories or principles to find solutions. In the context of our exercise, the student is presented with a scenario where they have to determine what grade they need on their 10th homework problem set to raise their average.

Now, let's apply the economic problem-solving steps to the homework scenario: Identify the problem (raising the average grade), gather data (current average and grades of completed sets), analyze the situation (using the calculation of averages), and propose solutions (determining the range of possible grades for the next set). By breaking down the problem into these steps, students can more easily navigate the complexities of economic decision-making, such as allocating their study time efficiently to aim for a grade that will raise their average.

Calculation of Averages

The calculation of averages is a fundamental concept not only in economics but also in various fields like mathematics and statistics. It's a measure used to find the middle or central value within a set of numbers. In our exercise, the student's average is a weighted mean where each homework set carries equal weight towards the final grade.

To calculate an average, sum up all the individual values then divide by the number of values. The formula for an average is: \[\text{Average} = \frac{\sum_{i=1}^{n}{X_i}}{n}\] where \(X_i\) is a value in the data set and \(n\) is the total number of values. In microeconomic education, averages can apply to various metrics such as cost averages, average revenue, or even average academic performance. Understanding how to manipulate averages is crucial for students as it essentially contributes to clear, problem-focused analytical skills.

Academic Performance Analysis

Academic performance analysis involves evaluating data related to student grades, participation, and overall achievement to understand and improve learning outcomes. In our exercise, analyzing academic performance means looking at the student's grades over the completed problem sets and using this data to forecast what is needed on the final set to achieve a desired outcome.

For instance, to maintain or raise their average grade of 88, the student should recognize patterns in their previous submissions. If they generally score above 88 when they study a certain number of hours, or if their lower scores are linked to specific types of economic problems, they could adjust their study habits accordingly. This analytical approach helps students take active steps toward achieving their academic goals, ensuring they are not just passive recipients of grades but are actively managing their educational journey.