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

The research question is clear and focused on two variables, which gives the exploration a strong starting point. Framing the task as “to what extent” also signals that the student is aiming to measure relationship rather than just describe it.

The introduction establishes context, but it stays broad and does not yet connect clearly to a method or hypothesis. The student should tighten the link between homelessness as a global issue and why gross monthly income is expected to be a relevant explanatory variable.

The student could briefly justify why these particular secondary sources are suitable and comparable across countries. A short reliability note would strengthen the logical development and help the reader trust the dataset.

The raw-data table is a useful foundation because it keeps the investigation anchored in original values before processing. Including the country, income, population, and homeless-percentage variables in one place supports the later analysis.

The processed-data table is structurally incomplete because the summary-statistic columns are not fully explained in the surrounding text. The student should define exactly what each grouped statistic represents and how it will be used in the analysis.

Grouping the countries into nine income bands is not justified here, so the transition from raw data to processed data feels arbitrary. The student should explain why these band widths were chosen and how they help answer the correlation question more effectively than the ungrouped data.

A final conclusion section would make the structure much stronger. The student could summarise the main numerical results, evaluate whether they support the original question, and then comment on any limitations of the method.

The graph title and axis labels are present, but the analysis would be clearer if the figure were directly matched to the intended statistic. Since the question is about correlation, a scatterplot of the original paired data would communicate the relationship more directly than a grouped display.

The student’s interpretation would be stronger if the graph section ended with a brief synthesis that explicitly answers the research question. A short statement linking the graph pattern, the summary statistics, and the overall extent of correlation would improve coherence.

This section heading promises a Pearson correlation analysis, but no calculation or interpretation follows. That breaks the logical flow of the exploration, so the student should either complete the analysis or remove the heading and replace it with a finished conclusion.

The references are a useful inclusion, but the student should make sure each source is consistently formatted and clearly tied to the data used. A more uniform reference list would improve the professional presentation of the investigation.

The notation is clear enough for the percentage calculation, but later formulas are not written with the same precision. The student should keep notation consistent throughout so the mathematics remains easy to interpret and verify.

The sample calculation is helpful because it shows the student’s working rather than only the final percentage. This makes the mathematical reasoning easier to follow and allows the reader to check the process.

Using grouped summary statistics alongside the raw values shows an attempt to represent the data in more than one way. That helps the reader compare central tendency and spread across income bands.

The written interpretation is understandable, but it would benefit from more precise statistical language. Rather than describing the graph generally as showing a relationship, the student should state the direction, strength, and any visible anomalies using consistent terminology.

The substitution step is difficult to follow because several terms are combined incorrectly, including expressions of the form $0.32\%+1.15\%$. The student should check each deviation carefully from $\bar{y}$ and show one clean squared-difference calculation per data value.

What feature of the data convinces the student that the relationship is negative, and how strong is that relationship compared with the scatter around the trend? Answering that quantitatively would make the interpretation much more convincing.

The standard deviation formula is written inaccurately, with sign and term issues in the squared differences. The student should rewrite the formula correctly and use the same structure consistently in the worked example, because formula errors undermine the credibility of the final result.

The figure communicates the intended variables, but it would be more effective if the relationship were shown with a clearer, more standard representation of paired data. For a correlation investigation, a scatterplot with a fitted line usually makes the pattern easier to interpret than a graph built from grouped values.

The explanation of the trend line is not mathematically secure because it refers to “exponential growth” without showing why that model is appropriate. The student should justify the choice of model and avoid overclaiming from a graph alone.

The introduction shows a clear personal connection to the topic by linking homelessness to the student’s experiences in Switzerland and Turkey. That personal context gives the investigation a genuine reason to exist rather than feeling randomly chosen.

How does the student’s personal interest in Switzerland and Turkey shape the choice of method as well as the choice of topic? Reflecting on that would help show a more distinctive personal approach.

Choosing real-world secondary sources and building a cross-country dataset shows initiative beyond a routine classroom example. The student is working with a substantial set of data, which is a positive sign of engagement with the topic.

The move from raw population counts to a percentage measure shows a sensible initiative to normalise the data. That makes the countries more comparable than using raw numbers alone.

To increase originality, the student could explain why the chosen summary statistics reveal something that the raw percentages do not. This would show that the processing step is purposeful rather than just added for completeness.

The decision to split the countries into nine groups appears procedural rather than independently justified. The student should explain why this was the best analytical choice, or consider a different method that more directly addresses the research question.

The student could show more initiative by comparing at least two statistical approaches, such as a scatterplot with Pearson’s $r$ and a brief comment on outliers. That would make the exploration feel more independently driven.

Leaving the Pearson section unfinished weakens the evidence of independent thinking because the exploration stops short of completing its own planned analysis. The student should finish the calculation or explain why a different statistic is more appropriate.

The student begins to reflect on the results by noting that the graph suggests a negative relationship. This is a useful first step because it shows the analysis is starting to move beyond description into interpretation.

A short evaluation paragraph would help the student connect the results back to the research question and state what was learned. That would make the reflection more substantial and show how the investigation changed the student’s understanding.

If the grouped data were replaced by the original ungrouped values, would the conclusion about the relationship change? Thinking about that would deepen the student’s reflection on the method itself.

Reflection remains too general because it does not evaluate the quality of the data or the impact of grouping on the results. The student should comment on limitations such as cross-country comparability, outliers, and whether the grouped approach may distort the relationship.

The discussion of the trend line is not yet critical enough because it treats the graph as confirmation rather than evidence to be tested. The student should question whether the chosen model genuinely fits the data and whether other explanations could account for the pattern.

Because the Pearson section is unfinished, the exploration does not yet reflect on what the mathematics has revealed about the relationship. The student should use the final statistical result to assess the strength of the correlation and compare it with the visual pattern.

Calculating homelessness as a percentage is an appropriate mathematical step because it makes the countries comparable on a common scale. That is a sensible choice for a relationship investigation.

The inclusion of a worked example for the percentage calculation shows that the student understands the need to demonstrate mathematical process, not just final answers. That improves transparency and supports later use of the results.

The mathematics selected here does not yet fully answer the research question because the correlation itself is not calculated. The student should use Pearson’s $r$, or another justified measure of association, rather than relying mainly on grouped summaries.

The student could strengthen the mathematics by showing one complete worked example for the grouped mean and one for the spread measure. This would make the processing easier to verify and would clarify how the summary statistics were produced.

The final standard deviation value is presented, but because the working leading to it is flawed, the result is not well supported. The student should verify both the arithmetic and the formula before using the value in later analysis.

The standard deviation work contains formula and substitution errors, so the final value cannot be trusted without correction. The student should recalculate from a correct formula and show the steps clearly enough for another reader to reproduce the result.

Would the same standard deviation result be obtained if each deviation were checked step by step from the mean? Reworking one group carefully would help the student identify where the calculation went wrong.

The graph does not fully exploit the mathematics available for a correlation investigation because it does not clearly show the paired data structure. A scatterplot with a fitted line would allow the student to interpret association more rigorously.

The trend line is discussed as if it proves an exponential relationship, but no mathematical justification is provided. The student should explain how the model was chosen and whether the fit is actually better than a linear alternative.

The interpretation of the graph is limited because it relies on visual impression rather than a completed correlation measure. The student should complete the Pearson calculation and use it to support or revise the conclusion.