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

The aim is too broad at this stage: it mentions whether predicted grades vary by study time, age, and gender, but it does not clearly state the exact statistical focus or how these variables will be compared. The student should tighten the wording so the investigation has a sharper, more testable line of development.

The student opens with a clear real-world motivation and a direct connection to the investigation theme, which helps the reader understand why the study matters. This gives the exploration a purposeful direction from the start and supports coherent development.

Consider trimming the extended formula explanations and replacing some of them with shorter, investigation-specific commentary on why each statistic is useful for this dataset. This would make the exploration more concise while keeping the mathematical purpose of each method clear.

The mode calculation is not logically matched to the data structure here. The formula shown is for grouped data, but the grades are discrete observations, so applying grouped interpolation weakens the reasoning chain. The student should use the actual most frequent grade rather than a grouped-class estimate.

The captioned summary table is well placed and makes the descriptive results easy to navigate. Grouping mean, median, mode, and standard deviation in one place supports a clear comparison across subjects and strengthens the internal structure of the presentation.

What specific evidence from the t-test allows the student to claim a statistically significant effect here, and how does that differ from the interpretation of the correlation coefficient? Clarifying that distinction would improve the logical flow of the analysis.

Some of the limitation discussion becomes too general, especially where broad statements are made about special needs and predicted grades without being tied back to the collected data. The student should keep the reflection anchored in the actual sample and methods used so the argument remains relevant.

The student defines the mean formula clearly and uses notation in a way that is easy to follow. This is a strong foundation for the later calculations because the reader can see exactly how the statistic is being constructed.

The median formula is written incorrectly: the expression should identify the middle data positions, not present them as a fraction in this form. The student should rewrite this using standard notation so the method is mathematically precise and unambiguous.

The notation in the mode calculation is inconsistent with the dataset and with standard statistical communication. Because the grades are not grouped into class intervals, symbols such as $l_0$ and $h_0$ do not describe the data clearly. The student should either regroup the data properly or use a discrete-data mode approach.

The sample standard deviation is shown through a complete chain of working, including the summed squared deviations and the final square root step. This is effective mathematical communication because the reader can verify the result rather than simply accepting it.

The interpretation table is useful, but it oversimplifies the meaning of correlation by treating every positive value as the same kind of relationship. The student should refine this by including strength bands that are tied to magnitude, not just direction, so later interpretations are more precise.

The correlation table would communicate more clearly if the variable coding were explained directly in the analysis rather than only in the table heading. For example, coding gender as female = 1 and male = 0 changes how $r$ should be interpreted, so the student should state that explicitly in the text.

The intermediate step $t=\frac{0.185}{0.1}$ is not justified clearly enough, so the calculation loses transparency. The student should show the denominator substitution explicitly before simplifying, which would make the derivation easier to check and more rigorous.

The regression equation is reproduced with an extra $y$ at the end, which creates ambiguity about the model. The student should write the equation exactly as $y=0.16x+5.11$ so the final model is communicated accurately.

The student’s personal connection to receiving predicted grades gives the investigation authenticity and makes the choice of topic feel genuinely student-driven. This is a strong example of personal engagement because the context is not generic; it arises from a lived academic experience.

Designing and collecting a survey from the school community shows initiative beyond using pre-existing data. This makes the exploration feel self-directed and helps the student build a dataset tailored to the research question.

The variable selection shows thoughtful personal judgement: the student does not only ask about grades, but also chooses gender, age, and study time in order to investigate possible influences. That choice gives the project a clear individual direction.

To push the investigation beyond a standard template, the student could explain why linear regression is the most suitable model for study hours rather than another option. A brief justification of the modelling choice would make the personal approach feel more deliberate.

The conclusion that study habits are the “strongest predictor” goes beyond what the current evidence can firmly establish. The student should be careful not to imply causal ranking unless the analysis compares effect sizes in a controlled way or explicitly acknowledges the limitations of correlation-based inference.

How might the interpretation change if students who study more also tend to take more demanding subject combinations? Considering that possibility would show stronger independent thinking about hidden influences on the results.

The student selects descriptive measures that are appropriate for comparing subject grade patterns, which shows good alignment between the mathematics and the aim. This makes the analysis relevant rather than purely procedural.

The mode calculation is not appropriate for these discrete grade values, so the mathematical method is misapplied here. The student should either identify the modal grade directly or explain why a grouped approximation is necessary, otherwise the result is not reliable.

Using Pearson’s $r$ followed by a t-test is a suitable SL-level way to evaluate linear association, and the student shows awareness of the inferential steps needed to move from correlation to significance testing.

The age t-statistic is not developed rigorously enough, because the substitution and simplification steps do not fully show how the stated value was obtained. The student should present the calculation more transparently so the result can be checked independently.

The results table is useful, but the interpretation appears inconsistent with the hypothesis-testing logic in the surrounding text. The student should check that the conclusion drawn from each t-value matches the critical value and tail choice being used.

The regression is based on aggregated mean points, which can inflate the apparent fit and weaken the mathematical validity of the model. The student should explain why aggregated data were used, or preferably test the relationship using the raw paired observations to make the model more defensible.

The regression graph and the reported $R^2$ value make the modelling step easy to interpret in context. Presenting both the equation and the coefficient of determination helps connect the mathematics to the strength of the relationship.

The analysis states that two variables reject the null hypothesis, but this conclusion needs to be tied more carefully to the exact test results and the decision threshold. The student should avoid summarising significance too quickly and instead show how each decision follows from the numbers.