IB Mathematics Applications & Interpretation (AI) SL Internal Assessment Example

The “Personal Code:” label appears without content, interrupting the flow; consider moving or populating it appropriately or omitting it if unnecessary.

The title and exploration subtitle are clear and informative, effectively conveying the investigation’s focus.

The detailed Table of Contents with clear section titles and page numbers enhances navigation and reflects deliberate organization.

Some entries use inconsistent punctuation and layout (e.g. ‘Statistical calculations.’ vs ‘Box Plots.’); ensure uniform formatting throughout the contents list.

When referring to Appendix Table 4, include a parenthetical reference (e.g. Table 4) to guide the reader directly to the supporting data.

Add axis titles and units to the box plot and ensure legible resolution to support the analysis visually and enhance presentation.

The quartile formula block is duplicated across two pages; remove redundancy to maintain conciseness and flow.

Ensure that figures are consistently numbered and captioned (e.g. Figure 1, Figure 2) to streamline cross-referencing and maintain presentation coherence.

The sentence ending with ‘and’ in the Data Collection section is incomplete, disrupting coherence. Revise to clearly state how the data subsets will be used.

Include a summary table defining each symbol (e.g. ${\overline{G}}_{Fk}$, ${\sigma }_{Sk}$) to avoid potential confusion when referencing formulas later.

The mean formula displays $\overline{G}=\frac{\Sigma g}{\Sigma }$ but uses an undefined \hat{\mathcal{U}} for sample size; replace with standard notation $n$ to maintain mathematical rigor.

The displayed formula $\frac{G_{Fk}-{\overline{G}}_{Fk}}{(G_{Fk}-{\overline{G}}_{Fk}{)}^2}$ is incorrect; please revise to show the intended calculation clearly (e.g. variance or z-score).

The outlier formula uses “U.0” which is undefined; revise to standard outlier notation (e.g. $Q3+1.5IQR$) for clarity.

Consider including a small table listing Q1, median, and Q3 values alongside the box plot to reinforce your descriptive analysis numerically.

The rationale for plotting first half goals on the horizontal axis and second half on the vertical axis is clearly stated, reflecting good mathematical communication.

The introduction interweaves the student’s passion for mathematics and football, demonstrating a clear personal approach that drives the investigation.

The contextual explanation of momentum shifts using in-match statistics adds depth to the analysis and demonstrates initiative in exploring confounding variables.

The narrative suggests significance from descriptive statistics; consider explicitly referencing the subsequent box plots or PMCC to substantiate the claim of a “significant difference.”

The investigation into why the Spain vs. France match is an outlier demonstrates critical analysis and personal engagement, enriching the exploration.

Include a brief sensitivity analysis comparing results with and without the outlier to quantify its impact on your overall conclusions.

The decision to remove the outlier is supported by contextual factors, demonstrating critical reflection and thoughtful consideration of data validity.

Variable notation such as ${\overline{G}}_{Fg}$ and ${\sigma }_{Fg}$ is introduced correctly but could be tabulated for clarity, ensuring consistent usage throughout.

The numerical calculations for ${\overline{G}}_{Fg}$ and ${\overline{G}}_{Sg}$ are accurate and appropriately interpret the difference in sample means.

The discussion effectively interprets the calculated standard deviations, linking numerical results to the spread and consistency of goals in each half.

The momentum figures are insightful but would benefit from accompanying numerical summaries (e.g. shot counts in text) to reinforce visual data interpretation.

Enhance the scatter diagram by adding a regression line to visualize the trend and support subsequent PMCC calculations more effectively.