Name: Carlos Cardenas
Maths PSMT
Name: Carlos Cardenas
Teacher: Ms Sosimenko Class: MAG111G
Course: 11 General Mathematics 2023
Unit: FIA2 Unit 2 PSMT
Student Number: 126
Word Count!
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Table of Contents
TOC o "1-3" h z u 1.0Introduction PAGEREF _Toc125217530 h 22.0Observations PAGEREF _Toc125217531 h 23.0Assumptions PAGEREF _Toc125217532 h 24.0The Plan PAGEREF _Toc125217533 h 24.1Concepts and Techniques PAGEREF _Toc125217534 h 24.2Use of Technology PAGEREF _Toc125217535 h 25.0Solution PAGEREF _Toc125217536 h 35.1Health Education Results PAGEREF _Toc125217537 h 35.1.1Measures of Center PAGEREF _Toc125217538 h 35.1.2Measures of Spread PAGEREF _Toc125217539 h 35.1.3Graph of Health Education results PAGEREF _Toc125217540 h 35.2Engineering Results PAGEREF _Toc125217541 h 35.2.1Measures of Center PAGEREF _Toc125217542 h 35.2.2Measures of Spread PAGEREF _Toc125217543 h 35.2.3Graph of Engineering results PAGEREF _Toc125217544 h 35.3Comparison PAGEREF _Toc125217545 h 35.4Solution PAGEREF _Toc125217546 h 36.0Evaluation PAGEREF _Toc125217547 h 46.1Reasonableness of Solution PAGEREF _Toc125217548 h 46.1.1Consideration of Results PAGEREF _Toc125217549 h 46.1.2Consideration of Assumptions and Observations PAGEREF _Toc125217550 h 46.2Strengths and Limitations of the Solution PAGEREF _Toc125217551 h 46.2.1Strengths PAGEREF _Toc125217552 h 46.2.2Limitations PAGEREF _Toc125217553 h 47.0Conclusion PAGEREF _Toc125217554 h 48.0Reference List PAGEREF _Toc125217555 h 59.0Appendixes PAGEREF _Toc125217556 h 69.1Evidence of Use of Excel PAGEREF _Toc125217557 h 6
IntroductionBrisbane 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.
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.
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.
The PlanConcepts and TechniquesThe 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.
Use of TechnologyThe 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.
SolutionWe 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.
Health Education ResultsMeasures of CenterCentral Tendency Formula Working Answers
Mean x=xn16933056.43
Median n+1258+60259
Mode Most occurring numberN/A 60
Standard Deviation =x-x2n-160 - 54.772+ 26 - 54.772+ + 53 - 54.77220.5
Range Maximum Q4- Minimum (Q0)97-1087
Interquartile Range Q3- Q1Q3 - Q1 = 69 - 44 = 2525
Upper fence Q3+1.5269 + 1.5 * 25 = 69 + 37.5
106.5
Lower fence Q1-1.5244 - 1.5 * 25 = 44 - 37.5 6.5
Determining 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
Engineering ResultsMeasures of CenterMeasures of SpreadCentral Tendency Formula Working AsnwersMean x=xn16933056.43
Median n+12(56 + 57) / 2 = 56.5
Mode Most occurring numberN/A 47
Standard Deviation =x-x2n-1(Variance) = (3743.9) 61.14
Range Maximum Q4- Minimum (Q0)87-10 77
Interquartile Range Q3- Q1Q3 - Q1 = 70.5 - 38 32.5
Upper fence Q3+1.5238 - 1.5 * 32.5 1.75
Lower fence Q1-1.5270.5 + 1.5 * 32.5 122.75
Determining 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.
Comparison-667001330810-350201426210-699401435570-317801524490-350201606930-764201714930-541001800610-65801911850-605801940290-47980201697092602210290-479802229370-379002343490-1428752569210-1174752841625028221200
SolutionThe 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.
EvaluationReasonableness of SolutionBased 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
Consideration of ResultsThe 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.
Consideration of Assumptions and ObservationsThe 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.
Strengths and Limitations of the SolutionStrengthsComprehensive 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.
LimitationsData 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.
ConclusionThe 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.
Reference ListLi, 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-185309Wilczek, F. (2023, June 12). Is mathematics like science pluralistic?[Blog post]. Scientific American.https://blogs.scientificamerican.com/cross-check/is-mathematics-like-science-pluralistic/
Symbolab. (n.d.). Equation Calculator.https://www.symbolab.com/solver/equation-calculator
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