Comparing Groups Fairly

Overview

In this fourth lesson of the unit, students compare two or more groups using parallel dot plots, box plots and summary statistics. They build on previous work with representing and describing data, focusing on variation, overlap, unusual features, sample size and the limits of evidence.

Learning intentions

Students will:

• compare groups using visualisations and summary statistics
• describe typical values, spread, overlap and unusual features
• use statistical language to support claims with evidence
• recognise that samples may not represent a whole population
• distinguish association from proof of causation

Success criteria

• I can identify and compare typical values and spread.
• I can describe overlap, clusters, gaps and unusual values.
• I can support a comparison with values from a graph or table.
• I can explain why sample size, sampling method and context affect the strength of a conclusion.

Curriculum links

• Mathematics and Statistics: statistical investigations, data displays, measures of centre and spread, and communicating findings.
• Mathematics and Statistics: Mathsteasers, providing higher-order challenge and opportunities to deepen understanding.
• Mathematics and Statistics: Mathsteasers alignment, connecting challenging questions with familiar statistical content.
• Key competencies: thinking; using language, symbols and texts; managing self; participating and contributing.

Lesson structure (60 minutes)

1. 0–7 min · Hook and retrieval. Display two groups’ parallel dot plots, such as weekday and weekend sleep hours, using the opening comparison slides. Ask: “Which group gets more sleep, and how confident are you?” Students silently write one claim and one question, then share with a partner. Elicit that a visual impression is not enough: comparisons need evidence and context.

2. 7–17 min · Model statistical comparison. Use the comparison language slides to model reading a summary table alongside parallel dot plots and box plots. Think aloud while comparing median, range or interquartile range, overlap, clusters, gaps and unusual values. Record a comparison frame: “Group A has a higher/lower typical value because… The spread is… The groups overlap… This conclusion is limited because…” Students annotate a copy of the example on the comparing groups worksheet.

3. 17–32 min · Paired data investigation. Give pairs two authentic or class datasets, for example travel-to-school times by transport type or daily screen time for two age groups. Students use the prepared visualisations and summary table on the comparing groups worksheet to identify at least two similarities and two differences. They must include numerical evidence and label the comparison as strong, tentative or not supported. Circulate and ask, “Which statistic supports that statement?” and “What does the overlap tell us?”

4. 32–43 min · Gallery walk and critique. Display pairs’ annotated comparisons. Students complete a gallery walk using the gallery-walk prompts and leave one comment identifying strong evidence and one question about a limitation. Discuss fairness, sample size, sampling method, context and possible sources of variation, such as different collection times or self-reported data. Emphasise that a difference between groups does not prove that one variable caused the other.

5. 43–54 min · Independent evidence-based writing. Students select one dataset and write a two-group comparison paragraph on the comparing groups worksheet. Require a clear overall comparison, reference to typical value and spread, a comment on overlap or unusual features, and one limitation. Students should use cautious language such as “in this sample”, “suggests” and “may be associated with”, rather than “proves” or “causes”.

6. 54–60 min · Share and exit check. Invite two students to read contrasting paragraphs. Use the plenary and exit-question slides to revisit the opening claim. Students complete the final three questions on the worksheet: state one meaningful difference, cite supporting evidence, and explain why the data cannot prove causation. Collect responses for planning the next lesson.

Resources

• the complete comparison and discussion slide deck
• the comparing groups worksheet
• Two or more comparative datasets, including context and sample sizes
• Statistical software or spreadsheet with prepared parallel dot plots and box plots
• Projector or interactive display
• Student devices, if using digital data displays
• Coloured pens or highlighters
• Gallery-walk display space

Assessment

• During modelling and paired work, check whether students distinguish median, range and interquartile range and refer to actual values.
• Use gallery-walk comments and oral explanations to assess recognition of overlap, variation, sampling limitations and unsupported causal claims.
• Mark the comparison paragraph and exit response for an evidence-based claim, accurate statistical language, relevant numerical evidence and an appropriate limitation.

Differentiation

• Provide colour-coded displays, a labelled example and sentence frames: “The median for…”, “The groups overlap between…”, and “This evidence is limited because…”.
• Pair students strategically and provide a reduced dataset or pre-highlighted median and spread for students needing additional support.
• Allow students to discuss their comparison orally before writing; provide vocabulary banks and read instructions aloud for EAL learners and students with literacy needs.
• Extend students by asking them to judge whether a conclusion is supported, identify a possible confounding variable, compare sample sizes, and suggest a fairer sampling method.
• Challenge confident students to explain how an unusually large or small value affects the mean, median or perceived spread.