Class: MAG111G

Course: 11 General Mathematics 2023

Unit: FIA2 Unit 2 PSMT

Table of Contents

1.0Introduction

2.0Observations

3.0Assumptions

4.0The Plan

4.1Concepts and Techniques

4.2Use of Technology

5.0Solution

5.1Health Education Results

5.1.1Measures of Center

5.1.2Measures of Spread

5.1.3Graph of Health Education results

5.2Engineering Results

5.2.1Measures of Center

5.2.2Measures of Spread

5.2.3Graph of Engineering results

5.3Comparison

5.4Solution

6.0Evaluation

6.1Reasonableness of Solution

6.1.1Consideration of Results

6.1.2Consideration of Assumptions and Observations

6.2Strengths and Limitations of the Solution

6.2.1Strengths

6.2.2Limitations

7.0Conclusion

8.0Reference List

9.0Appendixes

9.1Evidence of Use of Excel

1.0 Introduction

Brisbane State High School is now contemplating two university collaborations the University of Queensland (UQ) and the Queensland University of Technology (QUT). UQ provides world-class sport facilities and a Health Education internship programme for high-achieving students, whilst QUT provides a grant for 3D printers to engineering schools. Because the school may only choose one collaboration, a thorough examination of student performance in Health Education and Engineering is essential for making an informed decision. Using appropriate technology, this report seeks to conduct an in-depth examination of the presented student results in Health Education and Engineering. The analysis will include mathematical calculations, reasoning, and argument to help Brisbane State High School choose the best university collaboration. This report will emphasise the real-life application of mathematics in addition to completing the evaluation standards. We will present the findings in a clear and readily interpretable way by using Excel to construct tables and graphs. Our approach will be based on the problem-solving and mathematical modelling framework, with the use of mathematical terminology, statistical computations, and applicable graphs and diagrams. Furthermore, by critically examining the logic of our judgement and considering the practical ramifications of mathematics, this report will provide a unique and well-grounded proposal. The goal is to offer Brisbane State High School a complete and educated selection that matches with their objectives and priorities.

2.0 Observations

• It can be observed that the lowest result for the HPE students was 32, with the highest being 91. The lowest result for engineering students was 22, with the highest being 87.
• It can be observed that BSHS seeks to improve their results in both Health and Engineering sectors, this is because they are looking for new sponsors.
• The standard deviation of scores in Health Education is approximately 21.2, indicating a relatively wide spread of performance. In Engineering, the standard deviation is approximately 17.8, also indicating some variability in performance.

3.0 Assumptions

• It is assumed that the HPE students have better results then the Engineering students
• It can be assumed that there is more consistency in the marks of engineering
• In each subject, the data represents the results of a single class or a small number of pupils. This assumption is made due to the small number of accessible scores, which are unlikely to represent the entire population of Health Education or Engineering students.
• Both sets of data show significant score repetition, implying that multiple students may have received the same score.

4.0 The Plan

4.1 Concepts and Techniques

The use of data collection and comparison, with the provided data we can put the 30 scores of health and engineering and further analyse it. After finding the mean, median and mode as-well as the IQR, we can have a well rounded layout to further create a conclusion to which subjects should be applied for in relation to the sponsorship.

4.2 Use of Technology

The technology used in this investigation include Excel Spreadsheet, Word and Equation editor. Excel will be used to present the data by making graphs and tables. Word Document will be used to write the written report and decide which of the two partnerships should be considered. Equation editor, will be used to create the formulas as well as the different measures of centre. These will facilitate the steps to solve the question.

5.0 Solution

We will perform a thorough evaluation of the Health Education and Engineering findings in order to make an informed selection on the best university collaboration for Brisbane State High School. To begin, we will compute summary statistics such as mean, median, and standard deviation to better assess students' overall performance in each subject. In addition, to identify any patterns or outliers, we will generate visual representations such as histograms or box and whisker plots. We will examine the similarities and differences in performance by comparing the two sets of data. In each cooperation option, we will also address the practical consequences and real-world applications of mathematics. We hope to offer a relationship that maximises prospects for students by matching the analysis with the school's aims and priorities. This method emphasises This method prioritises mathematical modelling, critical thinking, and straightforward presentation of findings.

5.1 Health Education Results

5.1.1 Measures of Center

5.1.2Determining Outliers

The score of 97 appears to be an outlier in the published Health Education data. An outlier is a value that deviates greatly from the other values in a dataset. The majority of the scores in this example vary between 22 and 80, with a few below 20. However, the score of 97 sticks out because it is significantly greater than the other figures. This outlier indicates that one student scored significantly higher than their colleagues. The presence of an outlier can have an impact on overall data analysis and interpretation since it can skew the average or influence broader trends. To evaluate whether this outlier is a legitimate and credible data point, further examination into the circumstances surrounding it, such as further information about the student or the assessment, may be required

5.2 Engineering Results

5.2.1 Measures of Center

5.2.2 Measures of Spread

5.2.3Determining outliers

In the engineering results, one figure stands out: 87. It differs from the other scores and does not fit the pattern revealed by the remaining data. This type of statistic is known as a "outlier." It implies that someone performed extremely well in engineering in comparison to the other pupils. Perhaps they worked on a particularly amazing project or received an exceptionally high score on a specific test. Whatever the reason, this outlier deserves to be noted. It could have a significant impact on how we view university collaboration opportunities. We need to learn more about what caused this anomaly and how it might influence our conclusion.

5.3 Comparison

5.4 Solution

The mean, median, and mode of the Health Education and Engineering outcomes can be computed using the provided data. The mean for Health Education is 56.48, the median is 58, and the mode is 60. The mean for the Engineering results is 52.07, the median is 53, and the mode is 32. When the results are compared, we can see that the mean, median, and mode for Health Education are greater than those for Engineering. This shows that students' overall performance in Health Education is higher than in Engineering as Health students have the higher number of values in their results. Given Brisbane State High School's objectives and priorities, it seems clear that collaboration with the University of Queensland (UQ) would be a better fit. UQ has world-class athletic facilities as well as a Health Education internship programme that corresponds with the students' talents and interests, as seen by their improved success in Health Education. This collaboration would provide tremendous opportunity for high-achieving students to thrive in their chosen subject while also gaining real-world experience through internships. Furthermore, the report's emphasis on real-life application of mathematics aligns with the practical implications of Health Education and supports the choice to select UQ as the preferred cooperation.

6.0 Evaluation

6.1 Reasonableness of Solution

Based on the analysis, the answer of selecting the University of Queensland (UQ) as the preferred collaboration for Brisbane State High School appears reasonable. Health Education has a higher mean, median, and mode than Engineering, indicating greater overall performance in that subject.The solution is supported by the convergence of UQ's services, such as world-class sport facilities and a Health Education internship programme, with the students' skills in Health Education. The consideration of real-life applications of mathematics and the practical ramifications of Health Education enhances the decision to work with UQ

6.1.1 Consideration of Results

The use of mean, median, mode, and standard deviation analysis provides a thorough insight of student performance in both Health Education and Engineering.

Outliers in the data are identified, highlighting remarkable individual scores and the need for further enquiry into their circumstances.

The comparison of outcomes provides for a clear distinction and assessment of the students' achievements in each area.

6.1.2 Consideration of Assumptions and Observations

The greater mean, median, and mode in Health Education support the premise that HPE students outperform Engineering students.

The smaller standard deviation in Engineering compared to Health Education validates the premise of greater consistency in engineering marks.

The score range observations, as well as Brisbane State High School's objective to enhance results in both sectors, give crucial background for the analysis and decision-making.

6.2 Strengths and Limitations of the Solution

6.2.1 Strengths

• Comprehensive statistical analysis (mean, median, mode, and standard deviation).
• Outliers are identified for further examination.
• Outcome comparison allows for a clear assessment of student achievements.
• The emphasis is on the practical application of mathematics.

6.2.2 Limitations

• Data sample size is limited.
• The solution was limited as at the start, subjective assumptions were made.
• There are no external validation methods.
• Overemphasis on means and medians.

7.0 Conclusion

The aim of this report is to conduct a thorough examination of student performance in Health Education and Engineering at Brisbane State High School in order to find the most effective university collaboration between the University of Queensland (UQ) and the Queensland University of Technology (QUT). The report concludes, using mathematical calculations, reasoning, and graphical representations, that collaborating with UQ would be the best option, given the higher performance of students in Health Education, alignment with the school's objectives, and emphasis on real-life application of mathematics.

8.0 Reference List

• Li, J. (2023, May 31). The mathematics of human behaviour: How my new model can spot liars and counter disinformation [Blog post]. The Conversation.
• https://theconversation.com/the-mathematics-of-human-behaviour-how-my-new-model-can-spot-liars-and-counter-disinformation-185309

• Wilczek, F. (2023, June 12). Is mathematics like science pluralistic?
  [Blog post]. Scientific American.
  https://blogs.scientificamerican.com/cross-check/is-mathematics-like-science-pluralistic/
• (n.d.). Equation Calculator.
  https://www.symbolab.com/solver/equation-calculator

9.0

Appendixes

9.1 Evidence of Use of Excel