Lesson 7: Measures of Center
Finding the middle ground: Mean, Median, and Mode.
🎯 Learning Intentions
- Calculate mean, median, and mode
- Understand which measure is best for different situations
- Analyze data range (spread)
🎥 Media Anchor (8 mins)
Video: Research Skills for Students
- When is median a better measure than mean for your dataset?
- How do outliers change what your "center" appears to be?
1. The Human Mean (10 mins)
Activity: Give 5 students different numbers of blocks. Ask them to "share them out until everyone has the same amount" without removing any blocks.
Explain: That final number is the Mean (Average).
2. Definitions & Practice (20 mins)
Work through examples with a simple data set (e.g., 2, 5, 5, 8, 10):
- Mean: Add all up, divide by count. (30 ÷ 5 = 6)
- Median: The middle number when sorted. (5)
- Mode: The most common number. (5)
- Range: Highest minus Lowest. (10 - 2 = 8)
Tip: "The Median is the bump in the middle of the road." "Mode is the Most."
3. Application (15 mins)
Look at your own investigation data:
- If you have category data (e.g., Red, Blue), you can only find the Mode.
- If you have number data (e.g., heights), you can calculate Mean, Median, and Range.
Task: Calculate relevant measures for your data.
4. Discussion (5 mins)
Why might the Mean be misleading if there is one huge outlier?
(e.g., If billionaire joins our class, the "average" wealth skyrockets, but median stays same.)
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will engage with this resource to develop statistical investigation skills — planning inquiries, collecting and analysing data, interpreting distributions, and communicating findings. Tūhuratanga (investigation) is framed as a tool for understanding our communities and environment in Aotearoa New Zealand.
Ngā Paearu Angitū — Success Criteria
- ✅ Students can identify an investigative question, collect relevant data, and display it clearly.
- ✅ Students can interpret statistical findings and discuss what they might mean for a real-world community or environmental context.
Differentiation & Inclusion
Scaffold support: Provide structured investigation frameworks (PPDAC cycle templates) for entry-level access. Offer partially completed data tables for students who need additional support. Extend capable learners by asking them to critique a statistical claim from a news article, or to design their own community data investigation.
ELL / ESOL: Pre-teach statistical vocabulary (median, mode, range, distribution, sample, population). Pair visual representations (graphs, tables) with plain-language explanations. Allow students to discuss statistical ideas orally before writing. Encourage use of home language for initial sensemaking.
Inclusion: Statistical investigation offers natural differentiation — all students can engage with the same real-world question at different levels of mathematical complexity. Neurodiverse learners benefit from structured, step-by-step investigation processes. Use collaborative group investigation formats that distribute roles (data collector, recorder, analyst, presenter).
Mātauranga Māori lens: Tūhuratanga — the practice of careful investigation — resonates deeply with mātauranga Māori. The maramataka is a sophisticated data system: tracking environmental patterns, seasonal cycles, and ecological indicators over generations. Iwi environmental monitoring — counting kaimoana populations, tracking water quality, observing bird migrations — is applied statistical thinking. Framing statistics within community and environmental inquiry connects data to mana whenua responsibilities.
Prior knowledge: Students should have basic familiarity with data displays (bar graphs, dot plots). No prior statistical investigation experience required — the PPDAC inquiry cycle provides accessible scaffolding for first-time investigators.
Curriculum alignment
- Statistics — Statistical Investigation: Plan and conduct investigations using the statistical enquiry cycle — determining appropriate variables and data collection methods; gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends; comparing distributions visually; communicating findings, using appropriate display.
- Statistics — Probability: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging uncertainty.