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

The introduction establishes clear relevance and purpose. This helps the exploration because the student explains why the topic matters beyond the classroom, giving the investigation a focused real-world context.

The period labels are not internally consistent with the data tables that follow. Each interval actually contains 11 annual observations, so the investigation should either relabel the intervals or justify the year counts clearly to avoid confusing the reader.

The student lays out the scope of the investigation clearly and early. This is effective presentation because the reader immediately knows what periods are being compared and why the analysis will move across distinct historical eras.

This sentence contains a wording error and an unclear reference to the appendix. The student should correct the phrasing and state precisely what Table 1 shows so the reader can follow the transition from summary statistics to supporting data without ambiguity.

The comparison is relevant, but the claim would be easier to trust if the student summarized the actual differences more explicitly. Consider adding the exact percentage changes in one sentence and explaining why they matter, rather than relying on a broad comparative statement.

The structure here becomes less coherent because the student shifts from plotting to a curve-shape judgment without enough explanation of how the decision was made. The exploration would read more logically if the model choice were compared against evidence, not just described as a visual impression.

This is a natural place to signal why the France comparison belongs in the investigation. A brief transition explaining what gap in the UK analysis this section addresses would make the overall structure feel more seamless.

The conclusion introduces a date range that does not match the earlier investigation and should be corrected. In a presentation criterion, consistency matters because the reader needs the final summary to align exactly with the scope established in the body.

The student uses appropriate statistical language to explain standardization before calculation. This is strong communication because the formula is introduced with a clear purpose, helping the reader understand why per-capita rates are needed.

The definition is accurate and relevant to the method being used. Clear terminology like this improves mathematical communication because it shows the student understands the role of the test before applying it.

The explanation is broadly on the right track, but the terminology is not precise enough. The student should distinguish between population standard deviation and sample standard deviation more carefully, because mathematical communication depends on using the correct symbol and definition consistently.

The term 'scatter plot' is being used imprecisely here. The graphs appear to plot each crime against time rather than one variable against another, so the student should name the representation accurately to avoid misleading the reader about what the plot can support.

The interpretation table is useful, but the student could strengthen communication by briefly stating the source or basis of the category cutoffs in prose. That would help the reader see how the thresholds are being applied to the calculated $r$ values.

This statement is too strong for the evidence shown here. The coefficient may indicate a strong positive association, but the student should avoid overstating it as proof of a relationship without clarifying what the plotted variables actually represent and whether the graph is truly a scatter plot of paired data.

The notation is mostly clear, but the student should keep the value consistent throughout the exploration. Earlier and later sections use different values for the same result, which weakens mathematical communication because the reader cannot tell which coefficient is intended.

The student shows a clear personal starting point by linking the investigation to a real news article and an authentic interest in criminology. This works well because it gives the exploration a genuine purpose rather than making the topic feel assigned.

The student demonstrates initiative by turning a public claim into a self-directed statistical inquiry. That move strengthens personal engagement because it shows the question was actively chosen and investigated, not just described.

What evidence would the student need before moving from a plausible idea to a defensible conclusion here? A question like this is useful, but it would be stronger if the investigation later tested the mechanism rather than leaving it as a speculative example.

The student is leaning on a personal hypothesis too strongly here. A correlation coefficient does not by itself support a crime-mechanism story like this; the explanation should be treated as a tentative idea and tested against evidence before being presented as support.

The student’s choice of France is a good extension, but the comparison would be stronger with a brief justification of why France is the best comparator. Consider explaining what makes it methodologically useful, such as population size, data availability, or similar reporting systems.

This is a promising direction for future work because it identifies a specific missing explanatory layer. The student could make it even more personal by naming one factor to investigate first, such as unemployment, policing changes, or wartime disruption.

The student shows meaningful reflection by recognising that historical data quality affects interpretation. This is effective because it demonstrates awareness that the mathematics sits inside a changing social and reporting context.

The reflection is present, but it stops at surprise rather than analysing what the result means. The student should explain how the p-value affects confidence in the comparison and what it does not tell us about the causes of the change.

The interpretation shows a limited critical analysis of hypothesis testing. A deeper reflection would question whether consecutive yearly observations satisfy the assumptions of the test, rather than treating significance as enough to settle the issue.

The student identifies a real limitation of the method rather than treating the test results as unquestionable. That kind of reflection improves the exploration because it shows the student is thinking about validity, not just computation.

How certain can the student be that population is the main driver here if the data have changing time gaps and inconsistent crime definitions? This question would push the reflection from a plausible explanation toward a more critical evaluation of competing factors.

The conclusion would be stronger if the student named one concrete statistical insight gained from the investigation. Reflection improves when it shows exactly how the mathematics changed the student's understanding, not just that it was interesting.

This is a good limitation to mention, but it remains general. The student should connect the limitation back to the actual time-series structure of the data and explain how that changes the trustworthiness of the reported correlations.

The student uses mathematics at an appropriate SL level and chooses a highly relevant normalization step. Converting raw counts to rates per 100,000 is essential here because it makes comparisons across periods much more meaningful.

The wording is mathematically imprecise because it suggests that 'people committed crimes' rather than that crimes were recorded. The student should use cleaner statistical language so the rate being measured is not confused with the people themselves.

This is a place where the student could strengthen the mathematics by linking the rate calculations back to the research question more explicitly. Consider explaining whether the increase is proportional, absolute, or both, and why that distinction matters.

The formula is incomplete as written and does not show the summation or division clearly enough. The student should rewrite it so the arithmetic structure is unambiguous, especially because the later calculations depend on the number of years being counted correctly.

The student selects relevant inferential methods and connects them to the data source. That is a strong mathematical choice because it shows an attempt to justify the use of summary statistics before applying hypothesis testing.

Using
0.05 is standard, but the justification is mathematically shaky. A significance level does not make a conclusion 'accurate' or guarantee 'little room for error'; the student should explain it as a chosen threshold for rejecting the null hypothesis.

The test decision is overclaimed. The student can conclude that the null hypothesis is rejected at the chosen significance level, but should avoid wording that suggests the alternative hypothesis is 'accepted' in an absolute sense or that the result proves a real-world cause.

The mathematics is being interpreted as evidence of a causal mechanism, which is not justified by correlation alone. The student should separate association from causation and explain that the coefficient only measures linear relationship, not whether one crime leads to another.

The conclusion goes beyond what the mathematics supports. The student has not shown a paired-variables correlation analysis for France in the main text, so this claim should be softened or backed by the actual coefficient before it is used as evidence.