1. Level 1 Multivariate Unit
4 credits
NCEA clarifications, 2015

2. Investigate a given multivariate data set using the statistical enquiry cycle
An understanding of the difference between sample and population is required at all levels.
Updated December 2014

3. Investigate a given multivariate data set using the statistical enquiry cycle
Data The provided data set is a sample from a named population. You choose both the category variable and the numerical variable.

4. Data You choose both the category variable and the numerical variable.
Investigate a given multivariate data set using the statistical enquiry cycle
Data You choose both the category variable and the numerical variable.

5. Investigate a given multivariate data set using the statistical enquiry cycle
Problem You pose your own investigative question. The question must involve a comparison, include the variable to investigate, specify the groups being compared, the population and the direction of the comparison.

6. Investigate a given multivariate data set using the statistical enquiry cycle
Problem A suitable question would be ‘Do New Zealand year 11 boys tend to be taller than New Zealand year 11 girls?’.

7. Analysis You will create both a dot plot and a box and whisker plot.
Investigate a given multivariate data set using the statistical enquiry cycle
Analysis You will create both a dot plot and a box and whisker plot.

8. Investigate a given multivariate data set using the statistical enquiry cycle
Analysis The dot plot enables you to ‘see’ the distributions and discuss the features they notice.

9. Investigate a given multivariate data set using the statistical enquiry cycle
Analysis The box and whisker plot enables you to make a ‘call’ as evidence to answer your question for the given population.

10. Investigate a given multivariate data set using the statistical enquiry cycle
Analysis When ‘discussing features of distributions comparatively’ use the visual evidence in the displays.

11. Investigate a given multivariate data set using the statistical enquiry cycle
Analysis Comments about the features need to be comparative and in context of the numeric variable.

12. Analysis You could observe:
Investigate a given multivariate data set using the statistical enquiry cycle
Analysis
You could observe:
a larger spread in the middle 50% of the times to walk to school for year 10 students than for year 8 students that there is an overlap in the middle 50% of index finger lengths for year 11 girls and boys

13. Analysis You could observe:
Investigate a given multivariate data set using the statistical enquiry cycle
Analysis
You could observe:
that there is an overlap in the middle 50% of index finger lengths for year 11 girls and boys

14. Analysis You could observe:
Investigate a given multivariate data set using the statistical enquiry cycle
Analysis
You could observe:
that the middle 50% of heights of year 11 boys is higher up the scale than the middle 50% of heights of year 11 girls.

15. You must discuss features in context.
Investigate a given multivariate data set using the statistical enquiry cycle
Analysis
You must discuss features in context.
For example, identify the two groups being compared and refer to the variables by giving the numerical values and their units

16. Investigate a given multivariate data set using the statistical enquiry cycle
Analysis
Your discussion would need to be justified with supporting evidence from the displays and measures and there must be an understanding of the feature that is discussed.

17. Investigate a given multivariate data set using the statistical enquiry cycle
Conclusion
Answer the posed investigative question and make an informal inference about the population

18. Investigate a given multivariate data set using the statistical enquiry cycle
Conclusion
The answer to the investigative question needs to be consistent with the analysis that has occurred.
There needs to be evidence to justify the conclusion made.

19. Investigate a given multivariate data set using the statistical enquiry cycle
Conclusion
It is expected that the conclusion is consistent with the approach of looking at the medians and the relative location of the ‘boxes’ (middle 50% of the data).

20. Investigate a given multivariate data set using the statistical enquiry cycle
Conclusion
A small difference between the medians relative to the overall visual spread might not enable a call to be made and this would need to be identified.
In this case the consistent conclusion would be that it is not possible to make a call.