Te Kete Ipurangi Navigation:

Te Kete Ipurangi

Te Kete Ipurangi user options:

Senior Secondary navigation


Achievement objective S6-1

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

  • plan and conduct investigations using the statistical enquiry cycle:
    • A. justifying the variables and measures used
    • B. managing sources of variation, including through the use of random sampling
    • C. identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays
    • D. making informal inferences about populations from sample data
    • E. justifying findings, using displays and measures.


  • Uses the statistical enquiry cycle to conduct investigations:
    • Poses investigative questions.
    • Selects, uses and justifies variables and their measures to use in order to solve a problem. For example, if investigating how to improve the school canteen, students need to decide what ‘improve’ means and select data measures to capture improvement.
    • Selects and uses appropriate sampling methods, for example, systematic and simple random techniques (names drawn from a hat, dice, or random number generators).
    • Uses a variety of data collection methods, such as web survey, face-to-face questionnaire, and automated computer logs.
    • Collects and manages data.
    • Uses appropriate statistical graphs and tables to explore the data and communicates relevant detail and overall distributions.
  • Explores summary, comparative, bivariate, and time series data:
    • Links multiple representations and sees the connections between them.
    • Writes and presents a concise and informative report that includes communicating features in context; relevant summary statistics, graphs and tables to support the findings of the investigation; quantitative and qualitative statements; informal inferences about a population from a sample; justified conclusions.
  • See key mathematical ideas on NZmaths.

What is new/changed?

  • Justifying variables and measures used.
  • Looking at the different sources of variation, for example, measurement variation.
  • Random sampling.
  • Sampling variation.
  • Informal inferences using informal decision criteria as evidence for making a claim which is based on an understanding of sampling variation.
  • Alternative explanations for observed patterns in the data.
  • Contextual knowledge plays an important role in the entire statistical enquiry cycle.

Possible context elaborations

  • CensusAtSchool is a valuable website for classroom activities and information for teachers on all things statistics.
  • CensusAtSchool – data collected by students, about students, for students – investigating comparative and bivariate situations using the CensusAtSchool database. For example, Do the bag weights of year 11 girls tend to be heavier than the bag weights of year 11 boys in the 2009 CensusAtSchool survey? Is there a relationship between heights of students and their neck circumference?
  • Investigate the relationship between memory recall before learning memory recall skills and memory recall after learning memory skills.
  • Growing scatterplots – uses CensusAtSchool data and looks at relationships between neck and wrist circumferences:

Assessment for qualifications

NCEA achievement standards at level 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The following achievement standard(s) could assess learning outcomes from this AO:

  • AS91035 Mathematics and statistics 1.10 Investigate a given multivariate data set using the statistical enquiry cycle
  • AS91036 Mathematics and statistics 1.11 Investigate bivariate numerical data using the statistical enquiry cycle

Refer to the mathematics and statistics matrix.

Last updated October 21, 2013