Reading Data Displays

Overview

In this second lesson of the unit, students clean and organise the Week 1 dataset, then choose and compare displays that communicate different features of a distribution. They build on prior work with data types and statistical questions by considering which display is appropriate, how scale and intervals affect interpretation, and how technology can support—but not replace—mathematical judgement.

Learning intentions

• WALT organise and classify categorical and numerical data.
• WALT select appropriate displays for different types of data.
• WALT construct and interpret dot plots, stem-and-leaf plots, bar graphs, histograms and box plots.
• WALT use technology to generate, check and critique statistical displays.

Success criteria

• I can identify whether data are categorical or numerical and choose a suitable display.
• I can construct a display with an accurate title, labels, scale and key.
• I can describe clusters, gaps, peaks, outliers and the overall shape of a distribution.
• I can explain whether a display is an effective and truthful representation of the data.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge is connected to relevant mathematical content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: extension through reasoning, comparison and critique.
• Statistical investigations: organising, representing and interpreting data, with mathematical communication and critical thinking.

Lesson structure (60 minutes)

1. 0–5 min · Hook and retrieval. Open with the data-display introduction slides and show the same class data represented in two contrasting ways; students silently decide which display is more useful and justify their choice to a partner. Use mini-whiteboards for quick questions: “Is favourite music categorical or numerical?” and “Is height discrete or continuous?”

2. 5–15 min · Clean and classify the dataset. Display the Week 1 dataset and model checking missing values, inconsistent spelling, duplicate entries, units and impossible values; distribute the data displays practice worksheet. In pairs, students clean an assigned section, identify the variable type, and record what they changed and why. Pause to check that categorical values are grouped consistently and numerical values retain appropriate precision.

3. 15–27 min · Match data to displays. Revisit the data-display introduction slides to compare bar graphs for categorical data with dot plots, stem-and-leaf plots, histograms and box plots for numerical data. Students complete the display-matching task on the worksheet, selecting the most suitable display for each variable and explaining what the display reveals or hides; check responses through whole-class discussion rather than simply announcing answers.

4. 27–43 min · Construct and interpret. Model one numerical display from the cleaned dataset, emphasising title, variable labels, equal intervals, scale, units and an informative key. Students construct two different displays from the dataset on graph paper or the worksheet, then write three observations using the terms cluster, gap, peak, outlier, centre, spread and shape. Circulate with a checklist, asking: “What does this display make easy to see?” and “What could a reader misunderstand?”

5. 43–53 min · Technology critique. Demonstrate entering the data into a spreadsheet or CODAP and generating a display; use the data-display introduction slides for the critique prompts. Pairs compare their hand-drawn display with the technology-generated version, checking labels, scale, class intervals and omitted values. They identify one strength and one improvement, then investigate how changing histogram class intervals changes the apparent shape.

6. 53–60 min · Share and assess. Invite two pairs to share displays that communicate different features of the same distribution. Students complete the final worksheet reflection: “The best display for ___ is ___ because…” and “One feature I can see is ___.” Collect worksheets while students show a mini-whiteboard response to one final display-selection question.

Resources

• the data-display introduction slides
• the data displays practice worksheet
• Week 1 class dataset, including a cleaned-data copy for teacher use
• Graph paper, rulers and pencils
• Mini-whiteboards and pens
• Calculators
• Spreadsheet software or CODAP
• Display-matching and peer-feedback checklist
• Vocabulary wall or board space

Assessment

• Check mini-whiteboard retrieval responses and listen for accurate classification of categorical, discrete and continuous data.
• Observe pair work for correct cleaning decisions, suitable display selection, labels, scales and interpretation vocabulary; give brief feedback using the checklist.
• Review the worksheet practice and reflection for evidence that students can connect a data type and purpose with an appropriate display, and can identify features of a distribution.

Differentiation

• Provide a worked example, partially completed graph, graph templates and a vocabulary wall with visual examples of cluster, gap, peak, outlier, centre, spread and shape.
• Reduce the initial dataset for students who need less cognitive load, while retaining enough values to show a feature such as a cluster or gap.
• Pair students strategically and provide sentence starters: “I chose ___ because…”, “The distribution is…”, and “Changing the intervals makes…”.
• Support EAL learners with labelled model displays, consistent icons for categorical and numerical data, and opportunities to rehearse explanations orally before writing.
• Extend confident students by requiring them to justify competing display choices and explain precisely how changing histogram class intervals can create or obscure apparent patterns.