Seminar focus: argue which centre should be reported
Give groups the same dataset but different reporting recommendations. Speakers must anticipate counterarguments about outliers, skew, and context before the class agrees which measure best answers the question.
- Seminar move: Evidence-backed position line and rebuttal round
- Seminar outcome: A qualified recommendation naming when another measure would be better
🎯 Learning Intentions
- Calculate mean, median, and mode
- Understand which measure is best for different situations
- Analyse 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 "centre" 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
The class works cases where mean and median disagree, and argues which measure is honest.
Ngā Paearu Angitū — Success Criteria
- ✅ I can calculate mean, median, mode and range and interpret each.
- ✅ I can argue why one measure misrepresents a particular dataset.
Differentiation & Inclusion
Scaffold support: A dataset engineered so mean and median disagree sharply. Extension: construct data where the mode is the only honest measure.
ELL / ESOL: Work the calculations on the class's own numbers first.
Inclusion: Calculators throughout; the argument about which measure fits is what is assessed.
Mātauranga Māori lens: Choosing the measure that fits the question rather than the one that flatters the answer is an accountability practice.
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
This lesson develops the Level 4 statistical-investigation objective through a real stage of the PPDAC cycle. See the unit curriculum companion for the exact source statement and lesson-to-evidence map.