Comparing Data Sets

Overview

In lesson 23 of the 25-lesson unit Mapping Data and Change, students compare two data sets represented in tables and graphs. They select a suitable display, describe centre and spread using the median and range, support conclusions with numerical evidence, and identify limitations in the data or display.

Learning intentions

• WALT compare two data sets using tables and graphs.
• WALT describe a data set using a typical value and its spread.
• WALT choose an appropriate display for a purpose.
• WALT justify conclusions with evidence and recognise limitations.

Success criteria

• I can identify what a table or graph shows.
• I can find and compare the median and range of two data sets.
• I can use numbers from the data to support a conclusion.
• I can explain one limitation or question about the data.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that deepen mathematical understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge connected to familiar mathematics content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: reasoning, communication and problem-solving through non-routine data questions.
• Te Mātaiaho capabilities: students use mathematical reasoning, communicate evidence, and make informed judgements about data.

Lesson structure (45 minutes)

1. 0–5 min · Hook and notice. Open with the data comparison hook showing two class data sets with similar medians but different ranges. Ask: “Which group is more consistent, and how can we prove it?” Students silently notice two features, then share with a partner. Do not confirm answers yet.

2. 5–12 min · Explicit teaching. Use the centre-and-spread teaching slides to revise that the median is the middle value when data is ordered and the range is the greatest value minus the least value. Model comparing two small data sets: first describe the centre, then the spread, then write a conclusion supported by numbers. Emphasise that a graph can make patterns easier to see, but the display must have a clear title, labels and sensible scale. Students calculate the median and range of the model data on mini-whiteboards.

3. 12–17 min · Choosing a display. Reveal the display-choice prompts in the display selection slides. Discuss when a table, bar graph or line graph is useful. Explain that a line graph is suitable when values are measured across ordered time intervals, while a bar graph is useful for comparing separate categories. Students justify which display they would choose for two short scenarios and explain their choice to a partner.

4. 17–32 min · Partner investigation. Distribute the comparing data sets investigation worksheet to pairs. Students compare two data sets using the provided tables and graphs, calculate each median and range, answer interpretation questions, and write a conclusion using numerical evidence. They then identify a limitation, such as a small sample, uneven intervals, missing information, or a scale that could influence interpretation. Circulate and ask: “What does the centre tell you?”, “How do you know which set is more spread out?” and “What can’t this data tell us?”

5. 32–39 min · Evidence discussion. Display the discussion prompts in the evidence and limitations slides. Pairs compare answers with another pair, checking calculations and challenging whether each conclusion is supported by the data. Invite two pairs to share different conclusions and require each speaker to cite at least two values. Clarify that a higher median does not necessarily mean every value is higher, and a smaller range suggests greater consistency only within the data collected.

6. 39–45 min · Plenary and exit check. Return to the opening comparison using the plenary slides. Students independently complete the final question on the comparing data sets investigation worksheet: “Set A has a median of 12 and a range of 3. Set B has a median of 10 and a range of 9. Which set would you choose if you wanted results that were generally higher and more consistent? Explain using evidence.” Take responses as students leave or collect the worksheet for review.

Resources

• the complete data comparison slide deck
• the comparing data sets investigation worksheet
• Mini-whiteboards and pens
• Pencils, rulers and coloured pencils
• Calculators, if required for selected learners
• Optional classroom data or familiar contextual examples

Assessment

• Check mini-whiteboard calculations for accurate ordering, median and range.
• During pair work, listen for students distinguishing centre from spread and selecting displays for a reason.
• Mark the written conclusion and exit response for accurate calculations, numerical evidence and recognition of a limitation.

Differentiation

• Support learners with an ordered-data reminder, a worked median and range example, highlighted table headings, and sentence starters: “The median of ___ is higher than ___ because…” and “The range shows…”.
• Allow students to use counters or number cards to order values before finding the median. Pair learners strategically and read worksheet instructions aloud where needed.
• For EAL learners, pre-teach and display data set, median, range, centre, spread, consistent, evidence, and limitation, using diagrams and gestures alongside the words.
• Extend confident learners by asking them to create two different data sets with the same median but different ranges, then explain which display best reveals the difference and why.