IB Mathematics Analysis and Approaches (AA) HL Internal Assessment Example

The exploration opens with a clear section structure, and the progression from introduction to methodology and analysis is easy to track. This helps the reader understand the purpose of each stage before the calculations begin.

Some of the explanatory material here reads like a generic statistics handout rather than analysis tailored to the investigation. The student should trim broad definitions and keep only the procedural detail needed to justify the specific tests being used.

The transition from method to execution becomes drawn out because the explanation of critical values and test procedure is repeated in a very general way. The student should compress this section so that the reader reaches the actual data analysis more quickly.

The student explicitly reflects on the consequence of the bin requirement and notes that merging can mask differences between performance levels. This is a good example of evaluating a methodological compromise rather than ignoring it.

The explanation of degrees of freedom is descriptive, but it stops short of evaluating whether the choice of bins is statistically optimal. The student should consider how many degrees of freedom were lost and what that means for the power of the test.

The sectioning into “Comparing Male and Female Populations” and later “Testing For Independence” gives the investigation a logical two-part structure. That helps the reader see that each statistical method answers a different part of the research question.

A stronger reflection would briefly compare this independence test with an alternative approach, such as treating extracurricular hours as a quantitative predictor in a regression model. That would help the reader see why the chosen method is the most suitable one.

The repeated table caption numbering shows that the presentation still needs tighter organization. Reusing the same label for different tables can make later references confusing, so the student should ensure every table is uniquely numbered.

Because this table is central to the chi-squared conclusion, the student could improve readability by limiting the displayed intermediate values to the most informative figures. That would preserve the argument while reducing visual clutter.

The chi-squared conclusion is statistically correct, but the evaluation would benefit from discussing whether the significant result is practically important. A significant test alone does not tell the reader how large or meaningful the association is.

The regression discussion would be stronger if the student questioned the fit assumptions more explicitly. A trend line alone does not establish that a linear model is appropriate, so the student should discuss residual pattern, outliers, or heteroscedasticity before leaning on the regression interpretation.

The student does more than report a test outcome here: the scatterplot and regression line are used to interpret direction and strength, and the low $R^2$ is linked to a modest explanatory value. That shows thoughtful reflection on what the model can and cannot say.

If the outlying points were removed or if the GPA bands were defined differently, would the regression slope and $R^2$ still support the same conclusion? Reflecting on that would deepen the evaluation of robustness.

The conclusion is clearly signposted and returns to the original investigation after the analysis sections. This makes the overall structure feel complete and helps the reader locate the final claims quickly.

The limitations are relevant, but they are still mostly listed rather than analytically developed. The student should quantify how each limitation might bias the result, for example by explaining whether convenience sampling is more likely to inflate, deflate, or merely blur the observed relationships.

The future-work section would become more persuasive if each proposed extension were linked to a specific limitation. For example, a multi-school sample would address selection bias, while stratifying by grade would help test whether grade level is confounding the GPA–extracurricular pattern.