Studio checkpoint: choose measures that fit the data
Teams calculate mean, median, mode, and range where appropriate, then decide which measures belong in their project story. They test how outliers affect the result and record why any measure was included or rejected.
- Studio move: Measure comparison table and outlier stress test
- Portfolio evidence: An analysis memo justifying centre and spread choices
🎯 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
Ākonga choose between mean, median and mode on cases where the choice changes the answer.
Ngā Paearu Angitū — Success Criteria
- ✅ I can calculate mean, median, mode and range from my own data.
- ✅ I can say which measure fits my question, and why the others would mislead here.
Differentiation & Inclusion
Scaffold support: A dataset where mean and median clearly disagree, so the choice has consequences. Extension: construct data where the mean misleads and explain why.
ELL / ESOL: Teach mean, median, mode, range with the class's own heights or shoe sizes, not abstract numbers.
Inclusion: Calculators are fine; the reasoning about WHICH measure fits is the assessed part.
Mātauranga Māori lens: Choosing the measure that fits the question rather than the one that flatters the answer is an accountability practice, not just a maths one.
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
- Te Mātaiaho (2025) · Mathematics and Statistics · Phase 3 (Years 7–8) · Statistics (Practices): “- Planning and collecting data in order to respond to a statistical question (e.g. Are our feet the same length?) - Calculating the mean, median, and mode for numerical data - Calculating the range for numerical data”
- NZC (2007) · Mathematics and Statistics · Level 4: “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 displays.”
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.