Question

So far, a student has earned the following scores on four 100 -point tests this grading period: \(65,73,81,\) and \(82 .\) What score must the student earn on the fifth and last 100 -point test of the grading period to earn an average test grade of 80 for the 5 tests? F. 75 G. 76 H. 78 J. 99 K. The student cannot earn an average of 80 .

Short answer

Answer Choices: F. 85 G. 96 H. 99 J. 100 K. 105

Step-by-step solution

Calculate the total points earned so far

Add the scores of the first four tests: \(65 + 73 + 81 + 82\).

Calculate the total points needed for an average of 80

To have an average of 80 for the five tests, the student needs to have a total of \((\)80\text{ points})\times (5\text{ tests})=400$ points.

Determine the required score on the fifth test

Subtract the total points earned so far from the 400 points needed to achieve the desired average: 400 - (65 + 73 + 81 + 82).

Match the result with the given options

After finding the required score, compare it to the given options (F, G, H, J, K) to find the correct answer.

Key concepts

Arithmetic Mean

Understanding the arithmetic mean, commonly referred to as the average, is crucial when analyzing test scores. To find the mean score of a series of tests, you add up all the individual test scores and divide by the number of tests taken. This provides a single value that can reflect the overall performance on those tests.

For example, if a student has taken four tests with scores of 65, 73, 81, and 82, the mean score is calculated by adding these scores to get a total, which is 301 points in this case, and then dividing by the number of tests, which is 4. The result, 75.25, represents the average score up to this point. To reach a particular average, say 80, after five tests, the same principle applies: the sum total of all test scores divided by 5 should equal 80.

Test Score Improvement

Improving test scores is often a goal for many students. When a student is aware of their current average and has a target average in mind, planning becomes much simpler. Should a student wish to raise their average to a certain level, they must score above their current average on subsequent tests. It's a mathematical certainty.

Let's say a student's average after four tests is 75.25, but they aim for an 80 average. The fifth test score needs to be significantly higher than 80 to pull up the overall average. If you're working toward a specific goal, like lifting your average test grade, you might need to focus your studies on weak areas, employ test-taking strategies, or even seek additional help, such as tutoring, to ensure you achieve the necessary high score on your next test.

Academic Performance Analysis

Academic performance analysis often involves looking at test scores to assess a student's learning progress. By comparing a series of test scores, educators and students can identify trends, strengths, and areas in need of improvement. If there's consistent improvement in test scores, that indicates effective learning strategies and knowledge retention.

An important part of performing this analysis is setting benchmarks or standards, like an 80 average, and then measuring actual performance against this benchmark. Monitoring changes in performance after implementing new study habits or learning techniques can also provide valuable feedback for both students and educators concerning the effectiveness of these methods.

ACT Math Preparation

Preparation for the ACT Math section requires a strategic approach, as it covers a wide range of mathematical concepts from pre-algebra to trigonometry. Understanding how to calculate the arithmetic mean is just one skill that might be required. Students should practice various math problems and familiarize themselves with the test format.

Simulating testing conditions can help improve time management and reduce test-day stress. Additionally, reviewing commonly tested formulas and concepts, taking timed practice tests, and analyzing performance on these tests to identify areas for focus can significantly contribute to a more confident and prepared approach when tackling the actual ACT Math test.