To what extent is there independence between students' GPAs and the number of weekly extracurricular activities they participate in, and do average GPAs significantly differ between male and female students?HL
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5
Official IB Result
14/20
General feedback
14/20
0
10
20
No overall summary is available for this report.
4.1·Strength
Page 2
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.
4.2·Weakness
Page 3
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.
4.3·Weakness
Page 5
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.
4.4·Strength
Page 6
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.
4.5·Weakness
Page 12
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.
4.6·Strength
Page 12
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.
4.7·Suggestion
Page 15
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.
4.8·Weakness
Page 16
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.
4.9·Suggestion
Page 18
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.
4.10·Weakness
Page 18
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.
4.11·Weakness
Page 19
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.
4.12·Strength
Page 19
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 is linked to a modest explanatory value. That shows thoughtful reflection on what the model can and cannot say.
4.13·Question
Page 19
If the outlying points were removed or if the GPA bands were defined differently, would the regression slope and still support the same conclusion? Reflecting on that would deepen the evaluation of robustness.
4.14·Strength
Page 20
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.
4.15·Weakness
Page 21
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.
4.16·Suggestion
Page 21
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.
Criteria A: Presentation
3/4
0
2
4
Criteria StrandsPro
A.1Coherence and logical development
Good
A.2Organization and structure
Good
A.3Conciseness and relevance
Good
Criteria Feedback
- Your exploration follows a clear line of reasoning from the research question through data collection, testing, and conclusion.
- Your sections are well structured and easy to navigate, with a clear introduction, analysis, and ending.
- Your work stays mostly focused on the investigation and uses tables and figures to support the argument.
- Some explanatory passages are longer than necessary and interrupt the flow of the investigation.
- A few repeated or highly detailed tables reduce conciseness without adding much interpretation.
- The report would be even stronger if every section were tightened so that only the most relevant material remained.
Criteria B: Mathematical Communication
3/4
0
2
4
Criteria StrandsPro
B.1Mathematical language and notation
Good
B.2Multiple representations
Good
B.3Logical structure and clarity
Good
Criteria Feedback
- You use mathematical language correctly and generally consistently, including standard symbols and hypothesis-test notation.
- You make effective use of tables, formulas, and a scatterplot to present different parts of the analysis.
- Your writing usually guides the reader through the logic of each test clearly.
- Some notation could be kept more consistent throughout, especially when moving between words, symbols, and labels.
- A few sections feel more like generic instruction than direct communication of your own analysis.
- The report would be clearer if the numerical results were rounded more consistently.
1.1·Strength
Page 5
The chi-squared formula is written in standard notation and the variables are defined immediately afterwards. That consistency supports readability and makes the mathematical argument easier to follow.
1.2·Weakness
Page 7
The student does well to acknowledge the level of precision being used, but the report still carries too many digits in intermediate results. Rounding more consistently would improve clarity without weakening the mathematics.
1.3·Weakness
Page 14
The degrees-of-freedom expression for the two-sample t-test is presented clearly, but the notation could be tighter. Writing the sample sizes directly as and throughout would avoid the brief ambiguity created by switching between words and symbols.
1.4·Strength
Page 15
The chi-squared independence formula is stated in full generality before being applied to the table. This is effective mathematical communication because it connects the abstract rule to the specific data structure in the investigation.
1.5·Weakness
Page 18
The worked cell calculation is correct, but the report would be clearer if the notation for observed and expected values were kept consistent across the whole test. At the moment, the reader has to move between several slightly different labels to track the same quantities.
1.6·Strength
Page 19
The scatterplot legend and regression summary combine visual and symbolic information effectively. This is a strong use of multiple representations because it lets the reader interpret the direction of association and the size of the fit at a glance.
Criteria C: Personal Engagement
2/3
0
2
3
Criteria StrandsPro
C.1Independent thinking
Good
C.2Personal approach
Good
C.3Creativity and initiative
Good
Criteria Feedback
- Your investigation is clearly connected to personal experience and motivation, which gives it authenticity.
- You show initiative by designing a realistic school-based data collection approach and by using coding to reduce manual error.
- You make thoughtful choices about how to handle practical constraints in the data.
- The statistical approach is sensible but fairly conventional.
- There is room for more inventive use of the data or a more original analytical direction.
- Your project would show even stronger engagement if you explored a less familiar method or tested the data from another angle.
2.1·Strength
Page 2
The personal motivation is clearly rooted in the student’s own experience, which gives the investigation an authentic starting point. This helps explain why the question matters to the student rather than feeling externally imposed.
2.2·Strength
Page 3
The student shows ownership of the project by defining a realistic school-based population and designing the data collection around that context. That kind of independent framing is a genuine sign of engagement.
2.3·Weakness
Page 10
The method choices are sensible, but they remain fairly conventional. To push the investigation further, the student could justify why this particular set of tests is the most informative choice rather than simply the most familiar one.
2.4·Strength
Page 16
Using a Python program to sort the data for the contingency table shows initiative and helps reduce manual error. This is a practical example of independent problem-solving rather than relying only on hand calculation.
2.5·Question
Page 19
How might the interpretation change if extracurricular hours were split into several activity types instead of one combined measure? Considering that would show deeper independent thinking about the structure of the data.
2.6·Weakness
Page 21
The conclusion is thoughtful, but the investigation still follows a familiar statistical pathway with limited methodological originality. The student could strengthen personal engagement by experimenting with an additional analysis that is chosen because of the investigation’s unique context.
Criteria D: Reflection
2/3
0
2
3
Criteria StrandsPro
D.1Depth of reflection
Good
D.2Critical analysis
Good
D.3Evaluation of outcomes
Good
Criteria Feedback
- You reflect meaningfully on your findings and connect them back to the original questions.
- You acknowledge important limitations such as sampling, self-reporting, and the effect of binning decisions.
- You suggest sensible future improvements and extensions to the investigation.
- Some of the reflection is descriptive rather than deeply critical.
- The implications of alternative choices are not always explored in detail.
- Your evaluation would be stronger if you examined how different assumptions or methods might have changed the outcome.
Criteria E: Use of Mathematics
4/6
0
3
6
Criteria StrandsPro
E.1Relevance of mathematics
Good
E.2Level appropriateness
Moderate
E.3Understanding and accuracy
Good
Criteria Feedback
- You choose mathematics that is relevant to the questions you are asking and apply it appropriately to the data.
- Your calculations are generally correct, and your inferential conclusions match your test results.
- You use a coherent combination of statistical tools to address different parts of the investigation.
- Some methodological assumptions are not checked as fully as they could be.
- A few decisions, such as binning choices and the pooled comparison, would benefit from stronger justification.
- The analysis would be improved by including an effect size or confidence interval to deepen interpretation.
3.1·Strength
Page 3
The student clearly defines the population as “all students in grades 10 to 12 at my high school” and explains the sampling boundary. This makes the investigation mathematically grounded and helps the reader judge how far the conclusions can be generalized.
3.2·Weakness
Page 5
The normality check is treated as a standard chi-squared goodness-of-fit test, but the expected counts are generated from the sample mean and standard deviation. The student should address the effect of estimating parameters on the degrees of freedom; otherwise the test overstates its formal correctness.
3.3·Suggestion
Page 7
The sample mean and standard deviation are stated clearly, which is useful for reproducibility. To strengthen the mathematics, the student could briefly justify why these summary statistics are appropriate for constructing the normal model used in the goodness-of-fit test.
3.4·Question
Page 10
What alternative binning strategy would produce valid expected counts while preserving more information about the shape of the distribution? Considering that question would show stronger control over the method choice.
3.5·Weakness
Page 10
The bin-merging decision is sensible, but the write-up should be more explicit about how the merged categories affect the test’s sensitivity. Merging bins can hide local departures from normality, so the student should explain the trade-off rather than only stating the requirement of at least five per bin.
3.6·Weakness
Page 13
The pooled two-sample t-test is applied, but the equal-variances assumption is not checked in the investigation. The student should either justify pooling with evidence from the data or switch to a Welch-style comparison if the variances are not convincingly similar.
3.7·Strength
Page 14
The t-statistic is calculated in a clean, transparent sequence from the sample means and pooled variance. This step-by-step structure makes the inferential logic easy to follow and shows good command of the test procedure.
3.8·Suggestion
Page 14
The inference would be stronger if the student also reported an effect size or confidence interval for the mean difference. That would help distinguish statistical significance from practical significance, which is especially important when the observed difference is small.
3.9·Strength
Page 17
The expected-frequency formula is introduced and then applied correctly to a specific cell. This is good mathematical communication because the student shows both the general rule and its concrete use in context.
3.10·Weakness
Page 18
The chi-squared statistic is obtained correctly, but the analysis would be more robust if the student also commented on the size of the association, not just its significance. A measure such as Cramér’s V would add useful context to the conclusion.