IB MYP Mathematics: Reasoning with Data -- Practice Questions

These are original questions written for Marlbridge, modelling the kind of reasoning MYP Mathematics’s assessment criteria actually reward. They are not reproduced IB material – the IB holds copyright in its own subject guides and exemplars. Use these alongside official exemplars available through your school.

Related: Reasoning with Data study guide and revision notes.

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Section A

1. State which measure of central tendency is least affected by outliers, and why. [2]

2. State the difference between theoretical and experimental probability. [2]

3. Name a representation well suited to showing outliers in a data set. [1]

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Section B

4. A data set of 12 house prices on a street has a mean of $310,000, but one house recently sold for $1,200,000 while the rest are between $220,000 and $280,000.

(a) Explain why the mean is a misleading measure of central tendency for this data set. [2] (b) State which measure would better represent this data set, and why. [2]

5. A student is asked to find the probability of rolling a 6 on a fair six-sided die, and separately to find the experimental probability of rolling a 6 based on 60 rolls in which a 6 came up 8 times.

(a) Calculate the theoretical probability. [1] (b) Calculate the experimental probability from the trial. [1] (c) Explain why these two values are not expected to be identical, even though the die is fair. [2]

6. A student presents survey data on daily screen-time using only a bar chart of the mean screen-time by age group, with no comment on what the results suggest about the surveyed population.

(a) Identify which assessment criterion is weakest in this response, and why. [2] (b) Describe what should be added to strengthen it. [3]

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Section C

7. A student investigates recycling rates across five neighbourhoods, framed within the MYP global context of “globalization and sustainability.” They calculate the mean recycling rate correctly (Criterion A) and present a clearly labelled bar chart (Criterion C), but conclude only: “The mean recycling rate is 42%.” Explain what is missing relative to top-band Criterion D evidence, and rewrite the conclusion in outline to fix it. [6]

8. Explain, using a specific worked scenario, why “the mean is always the correct measure of central tendency to report” is not sound mathematical practice in this branch. [5]

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Worked answers

1. The median, because it is based on the middle position of ordered data rather than every value, so extreme outliers do not pull it up or down the way they pull the mean. [2]

2. Theoretical probability is calculated from the possible outcomes of a situation (for example, 1/6 for a fair die, since there are six equally likely outcomes). Experimental probability is calculated from the results of actually repeating a trial many times (the proportion of times an outcome actually occurred). [2]

3. A box plot (a scatter plot is also acceptable for bivariate outliers). [1]

4. (a) The mean is pulled sharply upward by the single $1,200,000 outlier, which is not representative of the other eleven houses; reporting $310,000 as “typical” would overstate what most houses on the street actually sold for. [2] (b) The median would better represent this data set, because it is based on the middle value of the ordered data and is not distorted by a single extreme outlier the way the mean is. [2]

5. (a) 1/6 (approximately 0.167 or 16.7%). [1] (b) 8/60 = 2/15 (approximately 0.133 or 13.3%). [1] (c) Theoretical probability describes the expected long-run proportion based on equally likely outcomes, but any actual finite trial (such as 60 rolls) is subject to random variation, so the observed experimental proportion will not exactly match the theoretical value except by coincidence – with more rolls, the experimental probability would generally be expected to get closer to the theoretical value, but a relatively small sample like 60 rolls can reasonably differ from it. [2]

6. (a) Criterion D (Applying mathematics in real-life contexts) is weakest, because top-band evidence requires drawing a valid, real-world conclusion from the data and reflecting on it, not just presenting a correctly calculated and clearly graphed statistic with no interpretation of what it means for the surveyed population. [2] (b) The response should add a concluding statement connecting the mean screen-time figures back to a real-world conclusion – for example, noting which age group shows notably higher or lower screen-time and what that might suggest – while also reflecting on limitations, such as whether self-reported screen-time is likely to be fully accurate, or whether the sample size and selection are representative of a wider population. [3]

7. Top-band Criterion D evidence requires drawing a valid, real-world conclusion from the data, reflecting on the conclusion’s reasonableness and limitations, and connecting it back to the task’s real-world context – here, “globalization and sustainability.” Stating only “the mean recycling rate is 42%” reports a correctly calculated statistic without any of this further reasoning. A stronger conclusion might read: “At a mean recycling rate of 42% across the five neighbourhoods studied, roughly two-fifths of household waste in this sample is being diverted from landfill, which is a meaningful contribution to the sustainability goals the global context addresses – but this conclusion is based on only five neighbourhoods within one area, and rates may vary considerably in neighbourhoods with different income levels, housing types or access to recycling infrastructure, so the finding should not be generalised beyond the specific sample studied without further data.” This connects the number to a real-world meaning, reflects on the model’s limitations, and explicitly names the relevant global context, rather than stopping at the statistic itself. [6]

8. Consider a small business’s employee salaries, where nine employees earn between $35,000 and $45,000 and the company’s founder earns $500,000. The mean salary across all ten employees would be pulled sharply upward by the founder’s outlying salary, producing a mean figure (well over $80,000) that does not represent what a “typical” employee at this company actually earns – reporting this mean as representative of employee pay would be seriously misleading. The median, based on the middle-ranked salary, would instead sit within the $35,000-$45,000 range where nine of the ten employees’ salaries actually fall, giving a far more representative single figure for this specific, skewed data set. This illustrates why choosing the correct measure of central tendency depends on the shape of the data – symmetric data is well represented by the mean, but skewed data or data containing outliers is better represented by the median – rather than defaulting to the mean as a universally “correct” choice regardless of data shape. [5]

Official syllabus

International Baccalaureate Organization, Middle Years Programme Subject Brief – Mathematics, from 2020, first assessment 2022 – the same source cited by the study guide and revision notes. Verified 2026-09-06.