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

The title is concise and directly reflects the research focus, aiding reader orientation at the outset.

The table of contents lacks page numbers, reducing navigational clarity; adding them would strengthen structure.

Empty cells in the contents table appear; remove or complete them to improve presentation coherence.

Definitions of external concepts (e.g., scatterplots) in the introduction add bulk; move them to the methods section.

Section headings would improve readability within the Mathematics section rather than a single block of text.

The data table spans two pages and even includes a blank row after Oregon; remove empty rows to maintain consistency.

Caption citation for the scatterplot is missing full source details; include complete attribution following a chosen style.

Conclusion neatly summarizes findings and ties back to the research question, showing coherence in development.

Bibliography entries are numerous but inconsistent in formatting; apply a uniform citation style (e.g., APA) for coherence.

The research question clearly specifies variables but could mention the year mismatch upfront for precision.

Method plan refers to “doing the outlier formula” but lacks detail on which dataset and order; specify the step-by-step sequence.

Consider adding additional representations (e.g., box plot, residual plot) to examine distribution and deviations more effectively.

Inconsistent Q₃ values (5.7 vs earlier 5.8) appear; maintain consistency to avoid confusion in statistical communication.

Column headers like “$x^2$” lack subscripts for individual observations (e.g., x_i²); use precise notation to enhance clarity.

The table is very dense and overwhelms the reader; consider summarizing key sum totals and moving raw data to an appendix.

Typo in the substituted formula uses “\sum 44” instead of “\sum x”; correct variable notation for accuracy.

The Pearson result is rounded to three significant figures correctly, demonstrating appropriate mathematical communication.

Hypotheses are described in prose; define H₀ and H₁ using symbolic notation to enhance mathematical precision.

Observed frequencies table is well labeled and supports the chi-square calculation clearly.

Grouping by mean values needs justification; discuss why splitting at 4.88 and 23.9 is statistically appropriate.

P-value source (TI-84 output) is not shown; include a screenshot or summary of calculator steps for reproducibility.

Personal anecdote about living in the “sunshine state” adds engagement but could be more tightly linked to methodology.

The extensive bibliography indicates thorough research across multiple sources, adding credibility to the exploration.

The rationale for Yates correction is briefly mentioned; expand on why small sample size warrants this adjustment.

All |O−E| values are identical (1.88); include commentary on why residuals are uniform across cells.

Identification of age as a confounding variable demonstrates critical reflection on study limitations.

Suggest designing a follow-up study with age-stratified incidence rates to address the highlighted limitation.

The aim statement precisely identifies x and y variables and methods, giving clear direction to the exploration.

Including all 50 states shows relevant mathematics at course level and completeness of data collection.

The narrative under 'Scatterplot' merely defines it; interpret key features (e.g., point clusters, trend line) to deepen analysis.

The IQR calculation uses Q₃ rather than Q₁ in the lower bound; ensure Q₁=3.8 is used for the expression Q₁−1.5·IQR.

The application of the 1.5 IQR rule is appropriate; the formula is clearly stated with correct notation.

Presenting the full xy, x², and y² breakdown in a table demonstrates a systematic use of mathematics for Pearson’s calculation.

The statement “0.0 < r < -0.3” is logically incorrect; use “-0.3 < r < 0.0” when describing a weak negative correlation.

Degrees of freedom formula is correctly applied, showing understanding of chi-square prerequisites.

Expected frequency calculations are correct, demonstrating thorough understanding of contingency table mechanics.

The computed χ² calc and p-value interpretation is correct, leading logically to failure to reject H₀.