Representing Data Clearly

Overview

In this seventh lesson of the Design a Sustainable Community unit, students turn their collected community data into meaningful displays and summary statistics. Working with their small project dataset, they select appropriate graphs, calculate mean, median, mode and range where suitable, and use evidence to make or refine sustainable design decisions.

Learning intentions

• WALT represent data appropriately using tables and graphs.
• WALT calculate and interpret mean, median, mode and range.
• WALT compare findings with the project requirements.
• WALT explain how data supports a fair and informed design decision.

Success criteria

• I can select an appropriate display for my data.
• I can label my graph correctly, including a title, axes, scale and units.
• I can calculate relevant statistics accurately.
• I can explain what the data suggests and acknowledge limitations or uncertainty.

Curriculum links

• Statistics — investigate data collection techniques and the practical implications of sampling, observation and experiments.
• Statistics — conduct investigations using samples, make fair inferences about a population and report findings with appropriate uncertainty.
• Mathematical modelling — interpret and communicate solutions in a practical community context, reviewing whether the model is suitable.
• Number and measurement skills — calculate and compare numerical summaries accurately.

Lesson structure (90 minutes)

1. 0–8 min · Hook and retrieval. Teacher displays two graphs showing the same community-preference data, with one graph using a misleading scale, through the hook and comparison slides and asks, “Which design decision might each graph encourage?” Students discuss what makes a graph trustworthy, then recall the meanings of mean, median, mode and range.

2. 8–20 min · Model appropriate representation. Teacher introduces the project dataset and models how to identify the variable type, choose a suitable display, label axes, select a sensible scale and include a clear title using the graphing workshop slides. Students help complete a decision pathway: categorical data may suit a column graph, while numerical data may suit a dot plot, column graph or other appropriate display; they justify the choice in one sentence.

3. 20–32 min · Guided statistics workshop. Teacher models ordering data before finding the median, identifying the mode, calculating the mean and finding the range, including how an outlier can affect the mean. Students use the worked examples in the data analysis worksheet to calculate statistics for a short shared dataset, checking answers with a partner and explaining which statistics are useful and why.

4. 32–58 min · Project data investigation. Teacher provides each pair with the project data collected in earlier lessons and conferences with students, prompting them to consider population, sample size, possible bias and uncertainty. Students complete the main section of the data analysis worksheet: organise their data, create at least one accurately labelled graph, calculate suitable summary statistics and write two evidence-based observations. Students may use a spreadsheet or graphing tool, with guidance from the step-by-step digital graphing slides.

5. 58–72 min · Design decision connection. Teacher displays the project requirements, such as reducing waste, conserving water or meeting community preferences, and models converting a statistical finding into a cautious recommendation. Students compare their findings with the requirements and write a recommendation using the frame: “Our data suggests … Therefore, we recommend … However, this may be limited because …” They identify whether their sample is sufficiently representative to support the recommendation.

6. 72–84 min · Peer feedback protocol. Teacher explains the feedback routine on the peer review and discussion slides: “Notice”, “Question” and “Suggest”. Students exchange graphs with another pair, silently inspect the display, then provide one strength, one question about accuracy or interpretation, and one improvement. Each pair revises one feature of its graph or explanation.

7. 84–90 min · Plenary and exit check. Teacher revisits the opening graphs and asks students to identify the misleading feature and explain how it could affect a decision. Students complete the final reflection and recommendation prompt on the final reflection section, then share one statistic that changed or strengthened their design thinking.

Resources

• the complete lesson slide deck
• the data analysis worksheet
• Project dataset from earlier investigations
• Project requirements or sustainable community design brief
• Graph paper, rulers, pencils and coloured pencils
• Calculators
• Laptops or tablets with spreadsheet or graphing software
• Whiteboard and markers
• Worked graph exemplars showing accurate and misleading representations

Assessment

• Observe retrieval responses and guided calculations; question students about why a particular display or statistic is suitable.
• Check each pair’s graph for an appropriate display, title, labelled axes, units, scale and accurate plotting. Review calculations and interpretation for evidence of understanding.
• Use the exit reflection to assess whether students can identify misleading representation, interpret a statistic and communicate a recommendation with an acknowledgement of limitations.

Differentiation

• Support students with graph exemplars, a display-selection decision pathway, preformatted tables in the scaffolded data analysis worksheet, partially labelled axes and a calculator. Provide guided prompts such as “The most common response is …” and “The range shows …”.
• For students requiring additional support, reduce the number of data points, provide a completed worked example and check each stage before they continue. Read instructions aloud and pair students strategically.
• Support EAL learners with visual examples, plain-language definitions and sentence starters for describing trends, comparing statistics and acknowledging uncertainty.
• Extension students compare two distributions using centre and spread, identify a misleading representation or outlier, and justify which statistic gives the fairest picture. They refine their final recommendation and explain what further data would improve confidence.

Extension

• Students create a second display of the same data and evaluate which representation communicates the finding most honestly.
• Students propose a follow-up sample or survey question that would reduce bias and improve the sustainability recommendation.