Year 8 Mathematics Statistics He Tātari Raraunga Social Context

Statistical Analysis of Treaty Settlement Data

Using statistics to understand patterns in Treaty of Waitangi claims and settlements — he tātari raraunga

Ingoa / Name

Akomanga / Class

Rā / Date

Ngā Whāinga Akoranga · Learning Intentions

I can calculate the mean, median, and mode from a dataset.

I can create and interpret bar graphs and dot plots to display data.

I can identify trends and patterns in statistical data and explain what they mean.

I can write a statistical conclusion that answers an investigative question.

I can explain why context matters when interpreting data about people and communities.

Context — He Tātari Raraunga

He tātari raraunga — statistical analysis of data

The Waitangi Tribunal investigates breaches of the Treaty of Waitangi. Since 1975, many iwi have lodged claims and negotiated settlements with the Crown. These settlements include financial compensation, land return, and cultural recognition.

Statistics helps us understand the scale and pattern of these settlements — how much was returned, how long claims took, and which regions were involved. Numbers alone don't tell the full story, but they help us see patterns that might not be obvious otherwise.

Data note: The figures in this handout are illustrative examples based on publicly available Tribunal settlement data (approximate values). Always check Te Ara, the Ministry of Justice, or the Waitangi Tribunal website for current official figures.

Statistical inquiry — PPDAC framework

We use the PPDAC cycle to guide our statistical investigation:

Problem — What question are we asking?
Plan — How will we collect and organise the data?
Data — What do the numbers show?
Analysis — What patterns can we find?
Conclusion — What can we say to answer the question?

Our investigative question:

Suggested question: "How have the financial values of Treaty settlements changed over time, and what patterns can we see in the data?"

Part A — The dataset

Here is a sample dataset of Treaty settlements (illustrative figures, NZD millions, rounded):

Iwi / Hapū	Year finalised	Settlement (NZD millions)	Region
Waikato-Tainui	1995	170	Waikato
Ngāi Tahu	1998	170	South Island
Pouakani	2000	4	Central North Island
Ngāti Awa	2005	42	Bay of Plenty
Ngāti Mutunga	2006	13	Taranaki
Affiliate Te Arawa	2008	13	Bay of Plenty
Ngāti Tūwharetoa	2018	135	Central North Island
Ngāti Hāua	2013	17	Manawatū-Whanganui
Rangitāne o Wairau	2014	14	Marlborough
Ngāti Kuri	2022	60	Northland

These figures are illustrative examples for learning statistics. Actual settlement values vary and include non-financial components (land, cultural redress).

Part B — Measures of centre

First, list all settlement values in order from smallest to largest:

Mean (average)

Add all values, then divide by the number of values (n = 10).

Sum of all values:

Mean = Sum ÷ 10:

Median (middle value)

With 10 values, the median is the average of the 5th and 6th values in your ordered list.

5th value:

6th value:

Median = (5th + 6th) ÷ 2 =

Mode

Which value appears most often? If no value repeats, write "no mode".

Mode =

Which measure best represents a "typical" settlement in this dataset? Explain your thinking:

Part C — Create a graph

Create a bar graph below showing settlement values (NZD millions) for each iwi. Label your axes, add a title, and mark the mean with a dotted line.

↑ Settlement value (NZD millions) | Iwi →

Extension: Create a second graph showing settlement values by decade (1990s, 2000s, 2010s, 2020s). What trend do you notice?

↑ Total settlements (NZD millions) | Decade →

Part D — Analysis and patterns

Answer these questions using your calculations and graphs:

1. What do you notice about the spread of settlement values? Are they clustered or spread out?

2. Which settlement is the highest? Which is the lowest? What is the range?

Range = highest value − lowest value = _______ − _______ = _______

3. The mean is much higher than the median for this dataset. What does this tell us about the distribution of values?

4. Look at the years of settlement. Is there a pattern in how many settlements happened in each decade?

Part E — Statistical conclusion

Write a conclusion that answers your investigative question. Use this structure:

My data shows that… [describe the overall pattern]
This is supported by… [quote specific numbers — mean, median, range]
An interesting finding is… [one surprising or important thing]
However, the data doesn't tell us… [limitations — what numbers can't show]

Why is it important to know the context when interpreting this data? (Think: what does each number represent beyond just a dollar figure?)

Curriculum alignment

Statistics — Statistical investigation: Plan and conduct investigations using the statistical inquiry cycle: gathering and cleaning data, displaying and identifying patterns, making statements, and communicating findings.
Statistics — Statistical literacy: Evaluate statements made by others about the findings of statistical investigations and data displays.
Social Sciences — Cultural identity: Understand how culture and identity influence people and communities, and how the Treaty of Waitangi shapes New Zealand's bicultural society.

NZ Curriculum Level 4 (Year 7–8). Integrates statistical inquiry with Aotearoa New Zealand histories.

Paearu Angitu · Success Criteria + Kaiako Planning Snapshot

Success criteria — ākonga will demonstrate:

Correct calculation of mean, median, and mode from given data
A clearly labelled graph that represents the data accurately
A written statistical conclusion that references context and manaakitanga towards the communities in the data

Te Ao Māori lens: Manaakitanga — treat the communities in the data with care and respect. Whanaungatanga — these settlements connect land, identity, and whānau. Tikanga guides how we interpret numbers about people.

Resources already provided. What to print: this handout (2 pages). Suitable for NZ kura and schools. Linked next step: Te Wānanga for a differentiated lesson plan, or save to My Kete.

Inclusion: ESOL / ELL ākonga — data presented visually with minimal text-heavy tasks. UDL / neurodiverse learners — chunked task sequence with explicit instructions. ADHD-friendly: short sub-tasks within each part.

Differentiation for teachers: Entry — pre-order data for students who need scaffolding. Extension — research one settlement in depth and compare the statistical and qualitative stories.

Teacher notes

Duration: 2–3 lessons. Part A–B in lesson 1, Part C–D in lesson 2, Part E in lesson 3 or as homework.
Sensitivity: Approach Treaty content with care. Acknowledge that numbers represent people, land, and justice. Whānau Māori students may have personal connections to this history.
Data literacy: Use this as a launching point to discuss what statistics can and cannot measure — financial figures don't capture cultural, spiritual, or environmental components of settlements.
Differentiation: Pre-order the data for students who need scaffolding. Extension: have students research one settlement in depth and compare the statistical picture with the qualitative story.
Cross-curricular: Strong links to Social Studies (Aotearoa NZ histories), English (report writing), and NCEA Level 1 statistics.
Real data: The Ministry of Justice and Waitangi Tribunal websites publish actual settlement figures. Students can update this dataset with current data as an extension activity.