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

The title effectively communicates the focus on Bechdel Test pass rates across genres and decades, providing clear context and scope for the investigation.

The definition of the Bechdel Test is repeated later; consider consolidating definitions into a concise statement to maintain flow and avoid redundancy.

In Table 1 the row for ‘To Kill a Mockingbird’ shows ‘0 Drama’ but formatting is inconsistent with other genre entries; standardize genre entries.

Graph 1 and Graph 2 lack axis labels and error bars; include annotations for scale, axis titles, and uncertainty to improve communication.

Table 3’s header appears as corrupted characters. Correct header labels for clarity and professional presentation.

Axis labels in the pass‐rate table omit the % symbol; including units improves clarity and consistency in mathematical communication.

Expected‐frequency table shows inconsistent decimal places (10.9 vs 8.29); standardize rounding to two decimal places for consistency.

The student’s personal motivation is well articulated, linking passion for cinema with the choice of Bechdel Test, demonstrating strong personal engagement.

Conclusion effectively summarizes trends and statistical findings, but reflection on the limitations of using only the Bechdel Test could be expanded.

The reflection acknowledges sampling biases but could deepen critical analysis by suggesting stratified sampling or alternative metrics beyond screen time.

The sample description notes 30 films per decade, yet later decade totals vary (e.g., 2020s has 22). Clarify sample counts to ensure consistency.

The calculation of σ is presented verbally; include the formula $\sigma =\sqrt{\frac{\sum (x_i-\bar{x}{)}^2}{n}}$ to enhance mathematical rigour.

The regression line $y=0.0789x-118$ is fitted to only seven data points; discuss validity of linear model assumptions (linearity, normal residuals).

The SMA formula is given as $\frac{x_1+x_2+x_3}{n}$ but does not explicitly define n; specify that $n=3$ to avoid ambiguity.

The moving average table omits explanation for first two decades; note why SMA is undefined for initial points to aid reader understanding.

The Chi‐Square test for trend is introduced but not specified; consider using the Cochran–Armitage trend test for categorical trend analysis.

Graph 3 interpretation is clear, but including a confidence band around SMA would strengthen the argument about stagnation periods.

In the contingency table for decades the 1960 row sums to 29 instead of 30, indicating a data‐entry error; verify counts for accuracy.

Some expected cell counts (e.g., Western) are below 5, violating ${\chi }^2$ assumptions. Consider combining categories or using Fisher’s exact test.

The computed ${\chi }^2=23.1$ is stated without the formula; include ${\chi }^2=\sum \frac{(O-E{)}^2}{E}$ to reinforce understanding of the calculation.

Genre contingency table includes underrepresented categories (Western n=3) which distort independence test; pool small genres or apply weighting before test.

Using Excel’s CHISQ.TEST to find the critical value is incorrect; this function returns a p‐value. Use CHISQ.INV.RT to calculate the critical threshold.

The rationale for weighting genres uses raw counts as weights without normalization; explain why this weighting reflects population proportions.

In Table 8 the pass‐rate column sums to 3.917 for an average >1; verify that the pass‐rate sum is correctly interpreted (should be average of proportions).