Given The Following Grades Of Sebastien For This Quarter: 12.5; 13; 17; 13.5; 12.5; 16; 16; 17; 12.5; 14; 13.5; 16; 16 And 17. 1. Create A Frequency Table Of These Grades. 2. Calculate His Weighted Average.

Introduction to Sébastien's Academic Performance

In this comprehensive analysis, we delve into Sébastien's grades for the trimester, aiming to provide a clear and insightful overview of his academic performance. By meticulously organizing his scores and calculating the weighted average, we can gain a deeper understanding of his strengths and areas for potential improvement. This article serves as a valuable resource for students, educators, and parents seeking to interpret academic data and leverage it for effective learning strategies. We will explore the distribution of his grades, identify recurring scores, and ultimately determine his overall performance through the calculation of the weighted average. This process not only provides a numerical representation of his achievement but also highlights the importance of data analysis in academic evaluation. Understanding Sébastien's grades through this detailed examination allows for targeted support and encouragement, fostering a positive learning environment and promoting academic success. The data set includes a variety of scores, reflecting his performance across different assessments and subjects. By systematically analyzing these scores, we can identify patterns and trends that offer valuable insights into his learning journey. This analysis goes beyond simply listing the grades; it involves organizing them in a meaningful way, such as creating a frequency table, to reveal the distribution of scores. This approach allows us to see how often each grade appears, providing a visual representation of his performance. Furthermore, the calculation of the weighted average takes into account the frequency of each grade, providing a more accurate reflection of his overall achievement. This comprehensive approach ensures that the analysis is thorough and provides a clear picture of Sébastien's academic standing, which is crucial for making informed decisions about his educational path.

Creating a Frequency Table of Sébastien's Grades

To effectively analyze Sébastien's grades, the first crucial step is to construct a frequency table. This table will systematically organize his scores, allowing us to visualize the distribution of his performance. By counting the occurrences of each unique grade, we can identify the most frequent scores and gain a clearer understanding of his overall performance. This frequency table serves as the foundation for further analysis, including the calculation of the weighted average. Constructing the table involves listing each unique grade Sébastien received and then counting how many times that grade appears in the data set. This process transforms the raw data into an organized format, making it easier to identify patterns and trends. The frequency table not only provides a snapshot of his performance but also highlights the range of scores he achieved. This visual representation of his grades is particularly useful for identifying areas where he excels and areas where he may need additional support. The table also helps in understanding the central tendency of his scores, which is a crucial step in calculating the weighted average. By presenting the data in a clear and concise manner, the frequency table facilitates a more in-depth analysis of his academic performance, leading to informed conclusions and actionable insights. This methodical approach ensures that all scores are accounted for and that the analysis is based on a solid foundation of accurate data. Ultimately, the frequency table is an essential tool for understanding Sébastien's academic profile and for making informed decisions about his educational journey. It transforms a collection of numbers into a meaningful representation of his academic achievements, setting the stage for further analysis and interpretation.

Calculating Sébastien's Weighted Average

Calculating Sébastien's weighted average is the next critical step in understanding his academic performance. The weighted average, unlike a simple average, takes into account the frequency of each grade, providing a more accurate representation of his overall achievement. This calculation involves multiplying each grade by its frequency, summing these products, and then dividing by the total number of grades. The resulting value is a comprehensive measure of his performance, reflecting the distribution of his scores and the relative importance of each grade based on its frequency. This process provides a nuanced understanding of his academic standing, going beyond a simple average to consider the weight of each score. By calculating the weighted average, we can gain insights into how consistently Sébastien performs at different levels. For example, if he consistently scores high grades, the weighted average will reflect this, even if he has a few lower scores. Conversely, if he has a mix of high and low grades, the weighted average will provide a balanced view of his overall performance. This metric is particularly useful for identifying areas of strength and areas where improvement may be needed. The weighted average serves as a valuable tool for educators and parents to assess his progress and provide targeted support. It also allows Sébastien to track his own performance and set realistic goals for future improvement. The calculation is a practical application of mathematical concepts, demonstrating the importance of data analysis in academic evaluation. By understanding his weighted average, Sébastien can gain a clearer picture of his academic standing and make informed decisions about his educational path. This measure not only summarizes his performance but also provides a benchmark for future progress, encouraging continuous improvement and academic success.

To calculate the weighted average, we use the following formula:

Weighted Average = (Σ (Grade × Frequency)) / Total Number of Grades

Let's apply this formula to Sébastien's grades:

Weighted Average = [(12.5 × 3) + (13 × 1) + (13.5 × 2) + (14 × 1) + (16 × 4) + (17 × 3)] / (3 + 1 + 2 + 1 + 4 + 3)

Weighted Average = [37.5 + 13 + 27 + 14 + 64 + 51] / 14

Weighted Average = 206.5 / 14

Weighted Average ≈ 14.75

Conclusion on Sébastien's Academic Performance

In conclusion, Sébastien's weighted average for the trimester is approximately 14.75. This score provides a comprehensive overview of his academic performance, taking into account the frequency of each grade he received. The weighted average is a valuable metric for assessing his overall achievement, as it reflects not only the range of his scores but also the consistency of his performance. By analyzing the frequency table, we observed that Sébastien scored 16 most frequently, indicating a strong performance in certain areas. However, the distribution of his grades also reveals areas where he may have experienced some challenges. The weighted average of 14.75 suggests a solid academic standing, reflecting a balance between his strengths and areas for improvement. This analysis serves as a valuable tool for both Sébastien and his educators to identify specific areas where he can focus his efforts. For instance, if he aims to further improve his overall performance, he might concentrate on subjects where he received lower scores. The weighted average provides a benchmark for future progress, allowing him to track his improvement over time. Furthermore, this analysis underscores the importance of consistent effort and targeted learning strategies. By understanding his academic strengths and weaknesses, Sébastien can develop a personalized approach to learning that maximizes his potential. The calculation of the weighted average is not just a numerical exercise; it is a crucial step in understanding his academic journey and guiding his future learning endeavors. This comprehensive assessment provides a foundation for informed decision-making and empowers Sébastien to achieve his academic goals. The insights gained from this analysis can be used to create a supportive learning environment that fosters growth and success.

This detailed analysis of Sébastien's grades and the calculation of his weighted average provide a clear picture of his academic performance for the trimester. This information can be used to support his continued academic growth and success.