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

The research question is explicit and comparative, which supports coherence throughout the exploration. The reader can immediately see the variables, the timeframe, and the two countries being contrasted.

The boxplot summary presents the quartiles and median clearly, which is strong mathematical communication. Using named statistics here helps the reader interpret the distribution rather than relying only on visual impression.

The student states that the boxplot shows the “mean amount of rainfall,” but a boxplot displays the median, quartiles, and spread rather than the mean. This should be corrected because using the right terminology is essential for accurate mathematical communication.

The variance and standard deviation section contains numerical inconsistencies: the Spain standard deviation is given as 31.7 mm here, but later the calculations use 30.6 mm. These values need to be reconciled because inconsistent numbers undermine the reliability of the analysis.

The written interpretation depends on the preceding incorrect calculation, so the conclusion about the Netherlands' spread is not trustworthy as written. The student should recalculate the value first, then explain what it tells us about variability.

The calculation shown here is incorrect: $23.0\times 1.20=27.6$, not 36.7. This is a significant arithmetic error because it affects the interpretation of the spread for the Netherlands.

The scatter plot is a good choice for showing how rainfall varies with year, and it appropriately introduces the correlation analysis that follows. This is a clear example of a representation matching the mathematical question.

The interpretation should be more careful: describing the Netherlands result as a “weak positive” relationship is fine, but the student should avoid overstating the strength when the coefficient is still close to zero. A brief numerical comparison with Spain would improve accuracy.

The explanation of Pearson correlation is mostly accurate and uses the correct symbolic range and terminology. This helps the reader understand how the coefficient should be interpreted in context.

The definition of Spearman correlation as a monotonic relationship is appropriate and shows stronger technical awareness. This is a useful distinction from Pearson and supports the student’s method choice.

The significance rule is stated backwards: if $p<0.05$, the result is statistically significant and the null hypothesis should be rejected, not accepted as “no significant relationship.” This conceptual error must be corrected because it affects the interpretation of every regression result.

The regression line is described in relation to its slope, which helps connect the visual pattern to the algebraic model. This is a good step toward interpreting the line rather than merely naming it.

This sentence is incomplete because it begins the explanation of p-values but is cut off before the logic is fully stated. The student should finish the rule clearly and use consistent language for significance decisions.

The student correctly reads a near-zero $R^2$ as indicating very weak explanatory power for year in the Spain model. That is an accurate statistical interpretation and helps justify the later conclusion.

The opening shows genuine independence in choosing a real-world comparison between Spain and the Netherlands rather than a generic textbook topic. This personal framing gives the investigation direction and makes later statistical choices feel purposeful.

The student gives a clear personal rationale for the topic, linking rainfall trends to travel experience and climate concerns. This works well because it shows why the investigation matters beyond the classroom and helps sustain a focused line of inquiry.

The interpretation links the boxplot to spread and outliers, which is a relevant use of descriptive statistics for comparing the rainfall distributions. This helps build a logical bridge from raw data to comparison.

The claim that the Netherlands has a higher “average” rainfall is not fully supported by the boxplot alone unless the mean is actually calculated and reported. The student should distinguish clearly between mean and median, and cite the statistic being used.

Describing the data as “stable frequency” is not enough to support claims about rainfall trend. Frequency by decile does not measure temporal change, so the student should avoid using it as evidence for fluctuation over time unless a clearer mathematical link is provided.

Using both Pearson and Spearman tests is a sensible methodological choice because it lets the student compare linear and monotonic association. That shows awareness that one statistic alone may not capture the full relationship.

The regression model is written clearly in symbolic form, and the variables are defined immediately afterwards. This is strong mathematical communication because it makes the model self-contained.

The hypotheses are stated explicitly, which is good practice for inferential mathematics. It shows the student understands that the regression test needs a clear null and alternative hypothesis.

The interpretation of $R^2$ is generally sound, but it should be tied more directly to the size of the explanatory effect. A low $R^2$ means year explains very little of the variation in rainfall, so the student should avoid implying any meaningful trend from this alone.