12 Statistics Classroom Activities with Real Data for AP Statistics, Cambridge 9709 and IB Teachers

In 30 seconds

Twelve practical statistics classroom activities, each with topic, level, timing, materials, steps, a worked example and discussion questions.
Students generate the data themselves, plus one published medical dataset for Simpson’s paradox.
The approach follows the American Statistical Association’s GAISE recommendations: real data, active learning and statistical thinking.
Levels are mapped to AP Statistics, Cambridge 9709 (S1/S2) and IB Mathematics.
All numbers in the worked examples have been checked, so you can use them as answer keys.

You have a syllabus that runs from box plots to chi-square tests, a class that switches off when the slides fill with formulae, and fifty minutes before the bell. You know students remember statistics better when they collect the numbers themselves, but planning a good activity takes time you do not have. Which activities actually work, and what do you do when the class data come out messy?

Below are twelve statistics classroom activities written up so you can run them next week. Each has a worked example with checked arithmetic.

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Why active, data-based statistics teaching works

The clearest guidance on teaching introductory statistics comes from the American Statistical Association’s GAISE reports. The 2016 GAISE College Report makes six recommendations: teach statistical thinking, focus on conceptual understanding, integrate real data with a context and purpose, foster active learning, use technology to explore concepts and analyse data, and use assessments to improve and evaluate student learning.^[1] Under the first recommendation, it stresses teaching statistics “as an investigative process of problem solving and decision making” and giving students experience with multivariable thinking.

The school-level framework, GAISE II (2020), describes statistical problem solving as four components: formulate statistical investigative questions, collect or consider the data, analyse the data, and interpret the results.^[2] It notes that “How tall is the plant?” has a single answer, so it is not a statistical investigative question; a statistical question anticipates variability, such as “How do heights in our class vary?”

Key idea Every activity below follows the same four-step cycle: ask a question that expects variation, collect the data in class, analyse it, then interpret it in context. If you name the four steps on the board each time, students start to see statistics as one method rather than a list of unrelated formulae.

Class data are never perfectly tidy, and that helps. When one value looks impossible, students learn to ask how the measurements were made and what design produced them, exactly as GAISE II encourages.^[2]

The 12 activities at a glance

Levels show where the content sits in each course (for Cambridge, the 9709 Probability & Statistics papers S1 and S2). Where a course does not list a technique, use the activity as enrichment.

#	Activity	Topic	Fits best	Time
1	Ruler-drop reaction time	Experimental design, matched pairs	AP; IB internal assessment ideas	40 min
2	Globe toss	Estimating a proportion, simulation	AP; 9709 S2; IB	30 min
3	Dice sampling distribution	Sampling distribution of the mean	AP; 9709 S2; IB	35 min
4	How many intervals capture the truth?	Confidence intervals	AP; 9709 S2; IB AI HL	40 min
5	Study-time survey	Chi-square test for independence	AP; IB Maths AI	45 min
6	Arm span vs height	Correlation and regression	AP; IB AA and AI	45 min
7	Word-list memory test	Two-sample comparison	AP; 9709 S1 (box plots)	45 min
8	Kidney stones	Simpson’s paradox, confounding	All courses	30 min
9	Journey to school	Quartiles, IQR rule for outliers	AP; 9709 S1; IB	25 min
10	Class heights	The normal distribution	AP; 9709 S1; IB	35 min
11	Can you taste the difference?	Hypothesis test, binomial	AP; 9709 S2; IB Maths AI	45 min
12	Misleading graphs clinic	Graph critique, communication	All courses	25 min

Teacher tip Keep one shared spreadsheet on the projector and type class data in as students call it out, so everyone analyses the same dataset. Save it: Activity 6 data feed Activity 10.

Activities 1–4: collecting data and simulation

1. Ruler-drop reaction time (experimental design)

Topic: matched pairs, randomisation, control. Level: AP Statistics; useful design practice for any course. Time: 40 minutes. Materials: one 30 cm ruler per pair, a recording sheet, a coin.

Ask the investigative question: “Is reaction time faster with the dominant hand?”
One partner holds the ruler at the zero mark just above the other’s open thumb and finger, then drops it without warning. Record the catch distance in centimetres.
Each student does three drops with each hand and records the median. A coin toss decides which hand goes first, so practice effects are balanced.
Compute each student’s difference (non-dominant minus dominant) and analyse the differences, not the two columns separately.

Classroom example A catch distance converts to time by t = √(2d/g). With g = 9.81 m/s², a 15 cm catch is √(0.30/9.81) ≈ 0.175 s. In one class of ten, the differences were 2, 1, 3, 1, 3, 1, 1, 3, 2, 2 cm. Mean difference = 1.9 cm, standard deviation = 0.88 cm. Paired t = 1.9 / (0.88/√10) = 6.86 with 9 degrees of freedom, p < 0.001. Strong evidence that this class catches the ruler sooner with the dominant hand.

Discuss: Why is matched pairs better than two separate groups? What would go wrong if everyone used the dominant hand first?

2. Globe toss (estimating a proportion with simulation)

Topic: sample proportion, sampling variability, confidence interval for p. Level: AP; 9709 S2; IB. Time: 30 minutes. Materials: an inflatable globe, a spreadsheet or calculator with a random-number function.

Ask: “What proportion of the Earth’s surface is water?” Students throw the globe around the room; on each catch, record whether the right thumb lands on water or land.
After 50 catches, calculate the sample proportion.
Simulate: generate many samples of 50 from a population with the accepted value (about 71% water) and look at how much the sample proportions vary.
Build a 95% confidence interval from the class result and compare it with the simulation.

Classroom example 36 of 50 catches were water, so p̂ = 0.72. Standard error = √(0.72 × 0.28 / 50) = 0.0635. 95% interval: 0.72 ± 1.96 × 0.0635 = (0.60, 0.84). In 10,000 simulated samples of 50 with p = 0.71, the standard deviation of p̂ was 0.064, matching the formula √(0.71 × 0.29 / 50).

Discuss: Is each catch truly random? How would 200 catches change the interval width?

3. Dice sampling distribution

Topic: sampling distribution of the sample mean, central limit theorem. Level: AP; 9709 S2; IB. Time: 35 minutes. Materials: five dice per group, or a dice simulator.

Each group rolls one die 30 times and plots a dot plot. The shape is roughly flat.
Now each group rolls five dice, records the mean of the five, and repeats 30 times. Plot the means.
Combine all groups’ means on one class dot plot. Compare centre, spread and shape with the single-die plot.

Classroom example A single fair die has mean 3.5 and standard deviation 1.708. The mean of five dice has the same mean, 3.5, but a standard deviation of 1.708 / √5 = 0.764. The flat shape becomes mound-shaped and the spread more than halves.

Discuss: Why does averaging reduce spread? Does the population have to be normal for the means to look normal?

4. “How many capture the truth?” (confidence intervals)

Topic: interpreting confidence level. Level: AP; 9709 S2; IB AI HL. Time: 40 minutes. Materials: a population you know, such as a spreadsheet of 1,000 values with a known mean, or a bag of numbered cards.

Keep the population mean secret. Each student takes a random sample of 25, builds a 95% confidence interval and draws it as a horizontal line on a shared board.
Reveal the true mean as a vertical line. Count how many intervals cross it.

Classroom example With 30 students, we expect 30 × 0.95 = 28.5 intervals to capture the mean. It surprises students that the chance of all 30 capturing it is only 0.95³⁰ = 0.215. The chance of 26 or fewer capturing it is 0.061, so a result like 27 out of 30 is entirely normal.

Discuss: Does any one interval have a 95% chance of containing the mean once it is calculated? What does “95%” describe? How would 90% intervals look on the board?

Common pitfall Students often say “there is a 95% probability the mean is in my interval”. Activity 4 shows why that is wrong: the mean is fixed and each interval either contains it or does not. The 95% refers to the method across many samples.

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Activities 5–8: relationships and comparisons

5. Study-time survey (chi-square test for independence)

Topic: two-way tables, expected counts, chi-square. Level: AP; IB Maths AI (SL and HL). Time: 45 minutes. Materials: a quick survey across two classes or year groups.

Ask: “Is preferred study time related to year group?” Each student chooses morning, afternoon or evening.
Build the two-way table and compute expected counts: row total × column total ÷ grand total.
Check that all expected counts are at least 5, then compute χ² and the p-value.

Classroom example Year 12 (25 students): 12 morning, 8 afternoon, 5 evening. Year 13 (25 students): 6, 9, 10. Expected counts are 9, 8.5 and 7.5 in each row. χ² = 3.73 with (2 − 1)(3 − 1) = 2 degrees of freedom, p = 0.155. There is not convincing evidence of an association, even though the table looks different by eye.

Discuss: Would 250 students with the same proportions change the conclusion? Is this sample random?

6. Arm span vs height (correlation and regression)

Topic: scatter plots, least-squares line, residuals, r and r². Level: AP; IB AA and AI. Time: 45 minutes. Materials: tape measures, masking tape on a wall.

Students measure height and arm span (fingertip to fingertip) to the nearest centimetre, barefoot, against a wall.
Plot arm span (y) against height (x), describe the pattern, then fit the least-squares line.
Each student calculates their own residual and interprets the slope in context.

Classroom example Ten students: heights 152, 158, 160, 163, 165, 168, 170, 172, 175, 181 cm; arm spans 149, 160, 158, 165, 163, 171, 166, 175, 174, 184 cm. The line is ŷ = −19.28 + 1.116x, with r = 0.966 and r² = 0.933. The student who is 170 cm tall with a 166 cm span has a predicted span of 170.5 cm, so the residual is 166 − 170.5 = −4.5 cm.

Discuss: What does a slope of 1.116 mean in words? Would you use this line to predict the arm span of a 120 cm child? What does a negative residual tell us?

7. Word-list memory test (two-sample comparison)

Topic: randomised comparative experiment, two-sample t-test or comparative box plots. Level: AP (two-sample t); 9709 S1 and IB for the descriptive comparison. Time: 45 minutes. Materials: two printed lists of 20 words, one in random order and one grouped by category.

Randomly assign students to List A (random order) or List B (grouped). Shuffle the sheets face down so nobody chooses.
Everyone studies for 60 seconds, waits 60 seconds, then writes as many words as they can recall.
Compare the groups with side-by-side box plots, then a two-sample t-test if your course includes it.

Classroom example List A recalls: 12, 9, 11, 8, 10, 13, 9, 11, 10, 12 (mean 10.5, s = 1.58). List B recalls: 14, 12, 15, 10, 13, 17, 12, 14, 11, 15 (mean 13.3, s = 2.11). Welch’s t = 3.36 with about 16.7 degrees of freedom, two-sided p = 0.004. Because the lists were randomly assigned, we can say grouping words probably caused better recall for these students.

Discuss: Why does random assignment allow a causal conclusion? Could the result depend on the words chosen?

8. Kidney stones (Simpson’s paradox with real data)

Topic: confounding, conditional proportions, multivariable thinking. Level: all courses. Time: 30 minutes. Materials: the table below on a slide or handout.

Show only the overall success rates and ask which treatment is better.
Reveal the split by stone size and ask students to explain how both comparisons can be true.

The data come from a 1986 British Medical Journal study of treatments for kidney stones, comparing open surgery with percutaneous nephrolithotomy (a keyhole procedure).^[3]

Stones	Open surgery	Keyhole (PCNL)
Small	81/87 = 93%	234/270 = 87%
Large	192/263 = 73%	55/80 = 69%
All	273/350 = 78%	289/350 = 83%

Classroom example Open surgery wins in both groups, yet keyhole surgery wins overall. The reason is stone size: large stones are harder to treat, and most of the open-surgery patients (263 of 350) had large stones, while most keyhole patients (270 of 350) had small ones. Stone size is the confounding variable.

Discuss: Which figure should a patient look at? Can you think of a school example, such as pass rates for two teachers with different classes?

Teacher tip This activity delivers the GAISE emphasis on multivariable thinking.^[1]

Activities 9–12: distributions, tests and critique

9. Journey to school (quartiles and the IQR rule)

Topic: five-number summary, box plots, the 1.5 × IQR outlier rule. Level: AP; 9709 S1; IB. Time: 25 minutes. Materials: each student’s journey time in minutes.

Collect journey times and sort them on the board.
Find the median and quartiles, then the fences Q1 − 1.5 × IQR and Q3 + 1.5 × IQR.
Draw a box plot with any outliers shown separately, and discuss whether outliers should be removed.

Classroom example Twelve times: 5, 8, 10, 12, 12, 14, 15, 16, 18, 20, 22, 45. Median = 14.5. Using the median of each half (the method on most graphic calculators), Q1 = 11 and Q3 = 19, so IQR = 8. Fences: 11 − 12 = −1 and 19 + 12 = 31. The 45-minute journey is an outlier, but it is a real student who lives far away, not an error.

Discuss: Should we delete the 45? How does it affect the mean compared with the median?

Common pitfall Quartile conventions differ between textbooks, calculators and software, so students may get slightly different answers. Agree a method with your class and tell students which method their exam board expects.

10. Class heights (the normal distribution)

Topic: normal model, z-scores, checking a model against data. Level: AP; 9709 S1; IB. Time: 35 minutes. Materials: height data from Activity 6 or a fresh measurement.

Draw a histogram of class heights and compute the mean and standard deviation.
Use the normal model to predict how many students should be taller than a given height, or within one standard deviation of the mean.
Count how many actually are. Discuss how well the model fits.

Classroom example Suppose a class of 30 has mean 165 cm and standard deviation 8 cm. For 180 cm, z = (180 − 165)/8 = 1.875, and P(height > 180) = 0.030, so we expect about 0.9 students, roughly one. Between 157 and 173 cm we expect 68.3%, about 20 students.

Discuss: Why might a class mixing two groups with different average heights show two humps? Does the model fit better in the middle or the tails?

11. Can you taste the difference? (hypothesis test)

Topic: null and alternative hypotheses, binomial probability, significance level. Level: AP; 9709 S2; IB Maths AI. Time: 45 minutes. Materials: two similar drinks (for example, two brands of bottled water or squash), small cups, blindfolds or screens. Check allergies first.

A volunteer claims they can tell the two drinks apart. State H₀: p = 0.5 (guessing) and H₁: p > 0.5.
Before tasting, agree the significance level (5%) and work out how many correct answers out of 10 would be needed.
Run 10 randomised trials. A coin decides which drink is poured each time, and the pourer is not the person recording.

Classroom example Under H₀, P(X ≥ 8) = 56/1024 = 0.0547 and P(X ≥ 9) = 11/1024 = 0.0107. So at the 5% level the taster needs 9 or 10 correct. Eight out of ten feels impressive but is not quite significant. This links to R. A. Fisher’s famous tea-tasting design, which used eight cups, four of each kind; a guesser identifies all four correctly with probability 1/70 ≈ 0.014.^[4]

Discuss: Why fix the critical region before tasting? What is a Type II error here? How would 20 trials change the test’s power?

12. Misleading graphs clinic

Topic: graphical communication, truncated axes, area distortion. Level: all courses. Time: 25 minutes. Materials: three or four graphs from newspapers, adverts or social media, plus one you have deliberately distorted.

In groups, students list everything that could mislead: axis start, scale, missing labels, 3D effects, cherry-picked periods.
Each group redraws one graph honestly and presents the before and after in one minute.

Classroom example A bar chart shows 52% and 55% with the vertical axis starting at 50%. The bars are 2 and 5 units tall, so the second looks 2.5 times bigger. The real ratio is 55/52 = 1.06: about 6% higher, or three percentage points.

Discuss: Is a truncated axis always wrong? Who benefits from each misleading graph?

Making the activities stick

Three habits turn a lively lesson into lasting learning.

Write it up in the four-step cycle. A one-page write-up (question, data, analysis, conclusion) makes good homework.
Use exit tickets. One question that tests the idea, not the procedure. For example: “A 95% interval is (0.60, 0.84). Write one correct and one incorrect interpretation.” GAISE recommends using assessment to improve learning, not just to grade it.^[1]
Return to the data. Reuse the heights and arm spans for regression, the normal model and outliers.

For AP Statistics, check the College Board’s Course and Exam Description for current unit order; experimental design, inference and chi-square tests all feature.^[5]

Teach more than one subject? All five teacher packs and every book for $79 (was $219).Complete Teacher Bundle · $79

If you would like the rest of the course planned to the same standard, the Statistics Teacher Pack gives you slides, lesson plans, worksheets, tests and exit tickets for all 16 chapters, with editable files you can adapt to your class. You can download the free sample first to see the format before you decide.

Frequently asked questions

Do I need special software for these activities?

No. A graphic calculator or free spreadsheet is enough. Start simulations with physical dice or cards, so students understand what the software then does faster.

What if my class data give a “wrong” result?

There is no wrong result, only one to interpret. If the ruler-drop shows no difference, discuss sample size and measurement error. Messy results are often the best lessons.

Which activities suit Cambridge 9709 students?

Activities 2, 3, 4, 9, 10 and 11 map directly to S1 and S2 content: estimation, sampling distributions, confidence intervals, box plots, the normal distribution and binomial hypothesis tests. Activity 8 is excellent for discussion of conditional probability.

Is it safe to run a taste test?

Use sealed, shop-bought drinks, fresh cups, and check allergies beforehand. Smell or sound tests work too.

References

Carver, R., Everson, M., Gabrosek, J., Horton, N., Lock, R., Mocko, M., Rossman, A., Rowell, G. H., Velleman, P., Witmer, J. and Wood, B. (2016). Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report 2016. Alexandria, VA: American Statistical Association. amstat.org
Bargagliotti, A., Franklin, C., Arnold, P., Gould, R., Johnson, S., Perez, L. and Spangler, D. A. (2020). Pre-K–12 Guidelines for Assessment and Instruction in Statistics Education II (GAISE II): A Framework for Statistics and Data Science Education. Alexandria, VA: American Statistical Association; Reston, VA: National Council of Teachers of Mathematics. amstat.org
Charig, C. R., Webb, D. R., Payne, S. R. and Wickham, J. E. A. (1986). Comparison of treatment of renal calculi by open surgery, percutaneous nephrolithotomy, and extracorporeal shockwave lithotripsy. British Medical Journal, 292(6524), 879–882. doi:10.1136/bmj.292.6524.879
Fisher, R. A. (1935). The Design of Experiments. Edinburgh: Oliver and Boyd.
College Board. AP Statistics Course and Exam Description. New York: College Board. apcentral.collegeboard.org