Finding the Centre

Overview

In this 45-minute lesson, students explore mean, median and mode as different ways to describe the centre of a data set. They build on earlier work organising and representing data, then calculate each measure and decide which is most useful for different sets of data.

Learning intentions

Students will:

• Calculate the mean, median and mode of small data sets.
• Explain what each measure tells us about a set of data.
• Compare measures of centre and identify the most useful measure for a given context.
• Communicate mathematical thinking using accurate vocabulary and evidence.

Success criteria

• I can order data and find the median.
• I can find the mode and explain when there may be no mode or more than one mode.
• I can calculate the mean by sharing the total equally across all values.
• I can justify which measure best represents a data set.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting challenge questions with relevant mathematical learning.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: reasoning, problem-solving and discussion through rich data questions.
• New Zealand Curriculum capabilities: thinking; using language, symbols and texts; managing self; relating to others.

Lesson structure (45 minutes)

1. 0–5 min · Hook and prior knowledge. Teacher opens the hook and retrieval slides with the data set 2, 3, 3, 4, 8 and asks, “What number best describes this group?” Students make a quick individual choice, then explain whether they used the most common, middle or fairly shared value.

2. 5–13 min · Teach the three measures. Teacher uses the teaching slides to define mode as the most common value, median as the middle value when data is ordered, and mean as the total shared equally; model 2, 3, 3, 4, 8, including the calculation (20 \div 5 = 4). Students record the definitions and help identify why the median requires ordered data.

3. 13–20 min · Guided comparison. Teacher displays the data sets 3, 4, 4, 5, 5, 6 and 1, 2, 2, 3, 12 using the guided comparison slides. Ask: “What are the mean, median and mode?” and “Do they all tell a similar story?” Students calculate with a partner, compare answers and discuss how the 12 changes the mean.

4. 20–33 min · Paired investigation. Teacher distributes the measures of centre investigation worksheet and reminds students to show working, order data before finding the median, and label each answer. Students complete progressively challenging data sets, including sets with no mode, two modes and an outlier. For each set they write one sentence explaining which measure is most useful and why.

5. 33–40 min · Mathematical discussion. Teacher uses the discussion and reasoning slides to present two contexts, such as shoe sizes in a class and weekly pocket money. Students compare answers with another pair, identify any differences, and justify whether mean, median or mode gives the fairest or most useful summary. Teacher prompts: “What does ‘typical’ mean here?” and “Would an unusual value affect your choice?”

6. 40–45 min · Plenary and exit check. Teacher displays the plenary and exit-ticket slide and asks students to respond independently: “For 2, 3, 3, 4, 20, calculate the mean, median and mode. Which measure best describes a typical value? Explain.” Students hand in their response as they leave.

Resources

• the complete mean, median and mode slide deck
• the measures of centre investigation worksheet
• Whiteboard and markers
• Calculators for selected learners who need support checking division
• Pencils, rulers and maths books
• Display screen or interactive whiteboard

Assessment

• Listen during the hook and guided comparison for correct use of “ordered”, “middle”, “most common”, “total” and “shared equally”.
• Check worksheet calculations and explanations, particularly whether students order data before finding the median and recognise the effect of an outlier.
• Use the exit response to identify whether students can calculate all three measures and justify a choice. Revisit any misconception in the next lesson.

Differentiation

• Support learners with smaller data sets, a number line, counters for physically sharing a total, and the sentence stems: “The ___ is useful because…” and “The unusual value affects the ___ by…”.
• Read worksheet instructions aloud, pair students strategically, and provide a partially completed worked example for learners who need reduced writing or processing load.
• Encourage students who finish early to create two data sets with the same mode but different medians, or the same median but different means, then explain how they achieved this.
• For EAL learners, keep the three definitions visible, pair each term with a simple example, and allow students to explain reasoning verbally before writing.