Statistical Mini Research, Essays (high school) of Mathematics

Analyzing the test scores of students

Typology: Essays (high school)

2022/2023

Uploaded on 06/05/2024

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Statistical Mini-Research on 4th Achievement Test
Scores in Math 10
Submitted by:
Mariae Kezziah T. Loayon
Submitted to:
Mr. Angelo Q. Delgado
I. Introduction:
Understanding student performance through statistical analysis is crucial in the field of
education. By analyzing test scores, educators can identify trends, measure student progress,
and pinpoint areas that need improvement. This mini-research focuses on the scores of the 4th
Achievement Test in Math 10, aiming to provide a detailed statistical overview of student
performance.
The objectives of this study are threefold:
To construct a cumulative frequency distribution table for the test scores.
To determine how many students fall into the third quartile, representing the top 25%
of the class.
To calculate key statistical measures, including the mean, median, mode, and standard
deviation of the scores.
These analyses will help in understanding the overall distribution of scores, highlighting the
academic strengths and weaknesses of the students. By examining these statistical metrics,
educators can make data-driven decisions to enhance teaching strategies, offer targeted
support to struggling students, and challenge high-achievers.
This research not only aims to provide insights into current student performance but also
serves as a benchmark for future assessments. By comparing these results with subsequent
tests, educators can track progress over time and adjust their methods accordingly. Overall,
this study is an essential step toward improving educational outcomes in Math 10, ensuring
that all students have the opportunity to excel.
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Statistical Mini-Research on 4

th

Achievement Test

Scores in Math 10

Submitted by: Mariae Kezziah T. Loayon Submitted to: Mr. Angelo Q. Delgado I. Introduction: Understanding student performance through statistical analysis is crucial in the field of education. By analyzing test scores, educators can identify trends, measure student progress, and pinpoint areas that need improvement. This mini-research focuses on the scores of the 4th Achievement Test in Math 10, aiming to provide a detailed statistical overview of student performance. The objectives of this study are threefold:

  • To construct a cumulative frequency distribution table for the test scores.
  • To determine how many students fall into the third quartile, representing the top 25% of the class.
  • To calculate key statistical measures, including the mean, median, mode, and standard deviation of the scores. These analyses will help in understanding the overall distribution of scores, highlighting the academic strengths and weaknesses of the students. By examining these statistical metrics, educators can make data-driven decisions to enhance teaching strategies, offer targeted support to struggling students, and challenge high-achievers. This research not only aims to provide insights into current student performance but also serves as a benchmark for future assessments. By comparing these results with subsequent tests, educators can track progress over time and adjust their methods accordingly. Overall, this study is an essential step toward improving educational outcomes in Math 10, ensuring that all students have the opportunity to excel.

II. Statement of the Problem: This research addresses the following specific problems:

  1. Constructing a cumulative frequency distribution table for the given test scores.
  2. Determining the number of students who belong to the third quartile.
  3. Calculating the mean, median, mode, and standard deviation of the test scores. III. Presentation of Data: The raw data consists of the following scores from the 4th Achievement Test in Math 10: 18, 23, 4, 14, 25, 15, 27, 21, 21, 19, 6, 22, 17, 20, 18, 25, 30, 27, 20, 20, 26, 21, 16, 28, 21, 21, 28, 19, 14, 22 IV. Data Analysis and Presentation: a. Cumulative Frequency Distribution Table The cumulative frequency distribution table for the given scores is as follows: b. Third Quartile The third quartile (Q3) represents the 75th percentile. To find Q3:
  • Sort the scores in ascending order: 4, 6, 14, 14, 15, 16, 17, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 23, 25, 25, 26, 27, 27, 28, 28, 30
  • Calculate Q3: 𝑄 3 = 0.75 × (𝑁 + 1 ) = 0.75 × 31 = 23. Thus, Q3 is between the 23rd and 24th values, which are both 25. Therefore, Q3 is approximately 25. There are 8 students (25, 25, 26, 27, 27, 28, 28, 30) belonging to the third quartile.

These results suggest that while the average performance is around 20, there is a moderate spread in the scores, with some students performing significantly better or worse than the average. The mode being 21 indicates that this score was achieved by the highest number of students, making it the most common score. Understanding these statistics is crucial for educators and administrators. The data indicates that while most students are performing around the average, there are outliers who may need additional support or enrichment. Identifying students in the lower quartiles can help target interventions to improve their performance, while students in the higher quartiles might benefit from more challenging material to keep them engaged. In conclusion, this detailed analysis provides valuable insights into student performance in the 4th Achievement Test in Math 10. By addressing the distribution of scores and key statistical measures, we can better understand the overall academic standing and identify areas for targeted improvement. This information is essential for developing effective teaching strategies and ensuring that all students have the opportunity to succeed.