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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It

3.9 Bivariate HOME | Achievement Objectives | Overview | Data sets & Variable Types | Introduction | Scatter plots | Excel | iNZight | Correlation Coefficient & Linear Model | The effect of Groups & Unusual Values | Predictions | Causality | Non-Linear Models | Discussion & Conclusion | Report Writing

Report Writing


Putting it all together

You will be given a data set with quantitative and qualitative variables.

Spend time researching and making wise variable choices that will allow lots of quality discussion when you do your report.

QUALITY not dribble.
A report any longer than 6 sides probably contains irrelevant waffle

use the Assessment checklist (Class notes)

How to reference research (link to

Ensure you are familiar with
1) Generic Assessment Instructions
2) Guidelines for the PPDAC cycle and Achieve / Merit / Excellence
3) Data Sets for practice

Class Practice Assessment
Complete an investigation on volcanic islands

The investigation is to be written as a report including:

1. An Introduction: Aim, Research Question, Definition of variables etc.
Evidence of research into the variables, relationship & context
Hypothesize & make a prediction as to possible relationships
Identify if variables are 'associated' or 'explanatory' and 'dependent'

2. Make Scatter-plot’s to investigating any relationship.
Discuss the relationship: type, association, strength, features.

3. Model (Linear)
Discussed & interpreted in context
Calculate and discuss the correlation coefficient 'r'
Investigate the effects of groups and outliers.
Interpolate and extrapolate data values.

4. Discussion
Possible assumptions, limitations, improvements, bias, and other models are possible?

5. Conclusion
Answer the Research Question
Research – Relate your findings to some research you have done
Summarise your findings
Evaluate the process


Class notes, Class notes
Class site

web links NZQA annotated exemplars 3.9 A | 3.9 A (Excel) | 3.9 B | 3.9 B data (Excel) (links to TKI resources)

AIS  p116

Ex 14.03
Sigma Example pg 299, answer p300 Excel data

McD's unit on Census & School | NZ incomes | Data sets with source and variable info for investigations. (and other data sets)

Quizlet on Scatterplots & Correlation

Class Exemplar:
Hawai'i Island Chain: Data csv, Information page |
Google Doc write up

Class Exemplar:
American New Cars 1993
Data csv, Information pdf |
Google Doc write up

Booklet pg 16 CHECKLIST


1) Generic Assessment Instructions:

Prior to the assessment you will be given information on the context.

You should do some research into to context to gain prior understanding to help during the assessment and have material to discuss in your report. You will be able to bring this contextual research into the assessment.

(get familiar with these)

You have been given data from...

Use the statistical enquiry cycle to carry out a statistical investigation to determine if there is a relationship between at least one pair of variables.

Write a report describing the investigation.

- Familiarise yourself with the data set provided. This will include doing research to help you understand the variables and develop a purpose for the investigation.

- Pose an appropriate relationship question that can be answered using variables in the data set. The variables you choose must be numerical, and the variable you use as your response variable must be continuous. You may choose to investigate more than one pair of variables. Select appropriate display(s) to graph your data.

- Identify features in the data, including the nature and strength of the relationship.
Find an appropriate model.

- Use your model to make prediction(s).

- Write a conclusion answering your question.

- Support your conclusion by referring to your analysis and/or features of the visual display(s). Include a reflection on your process, which could consider other relevant variables, or evaluate the adequacy of your model(s).

In writing your report, link your discussion to the context and support the statements you make by referring to statistical evidence.

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2) What is expected in your report

(based on the PPDAC cycle) This information in word version

(1) Pose a Question (Introduction)


- Investigate the relationship between two variables.
- Define the variables (and units)
- Describe the purpose for the investigation.
- Some reference to own research done (could be inferred)
- Comparative Research Question.

Merit / Excellence (Achieve and...)
- Make a prediction / hypothesis and justify your reasoning.
- Links made to research done (with references)
- Variables explained & researched.
- Consider several pairs of variables

How to reference research (link to

(2) Plan / Data

Intentions stated for investigation

Merit / Excellence (Achieve and...)
- Is the data representative of the population?
- Assumptions \ issues
- Issues of sample size
- Scatter plot matrix discussion
- Explain the reasoning behind choice of variable.


(3) Display & Analysis


- Scatter plots (with labels)
- Correlation coefficient 'r'
- Equation(s) of trend line(s)

(extension) Calculation and graph of Residuals.

(4) Discussion

Scatter plot:
- Correct variable placement
- Describe in context what the scatter plot shows (state the obvious)
- Trend. Linear or non-Linear and reasons why?
- Association. Positive or Negative and reason why?
- Strength. Weak, Moderate, Strong. Discussion of 'r' and reason why?
- Groups or clusters. Investigate possible reasons or causes.
- Unusual Values (any worth noting)
- Scatter Even or changing. Was this expected?
Discussion of the fit of the data through the range of 'x'

Merit & Excellence (Achieve and... )
- Justification of variable placement on scatter plot(s)
- Investigation into other groups or variable combinations
- Discussion of scatter plots of different scatter plots (variable combinations or groups)
- Identify and investigate outliers.
- Test robustness of model or effect of unusual values.
- Investigate alternative models.
- Predictions made, with discussion on precision.
- Choice of values to predict explained and relevance to wider population
- Interpretation of trend line gradient in context
- Discussion of the number of data points analysed
(extension: Residuals)

(5) Conclusion

Answer research question in context.

Merit & Excellence (Achieve and... )
- Link relationship to context.
- Compare findings to research.
- Discuss other factors worth considering.
- Discuss other relationships worth considering


Background information related to the data set will be provided. There should be sourcing of relevant contextual knowledge about the situation under investigation from places such as the internet, the school or local library, newspapers and magazines. These sources should be referenced in their report.

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Practice Data Sets

Progress check: Long jump data set

Progress check: Internet/GDP data set (Achieve & Merit - includes interpolation & extrapolation)

Analyse the Life Expectancy data


"Achieving in Statistics" by W. Geldof data sets. Practice Assessments, gradually becoming more self-directed.
If you have purchased the book from the student office for $16 you can have your very own answers and check your progress.

pg105 Flight Information | pg104 Plane Facts | pg110 Used Cars | pg111 United Nations | pg 114 Boat Data

Q2 Data
Q3 Data
Q4 Data

Q2 Ans
Q3 Ans
Q4 Ans


More data sets in EXCEL
Blood pressure | Cars | Cement hardness | Crackers | Creatine Kinase | Fisher iris | Incomes | Internet & GDP | January Temperature | Life Expectancy | Marriage Age | Mens Marathon | Olympic Long Jump | Optical Absorbance | Planets | Reaction Times | Road Conditions

Data Sets: | multivariate | Data Story Library | ConnectMV

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