S5-1: Plan and conduct surveys and experiments using the statistical enquiry cycle: determining appropriate variables and measures; considering sources of variation; gathering and cleaning data; using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets; comparing sample distributions visually, using measures of centre, spread, and proportion; presenting a report of findings.

Elaboration on this Achievement Objective

This means that students will use the statistical enquiry cycle to plan and conduct investigations. The cycle has five phases that relate to each other. Some enquiries follow these phases in sequence but often new considerations mean that a statistician must go back to previous phases and rethink. The phases are:

 Statistical investigation cycle.

At Level Five students should be able to pose suitable questions for data driven inquiry. The questions may be:
  1. Summary, for example, what is the normal height of a 14-year-old female?
  2. Comparitive, for example, do males do more exercise than females?
  3. Relational, for example, is there a relationship between television watching and lack of exercise?
Given a question or assertion, students need to decide on appropriate variables, for example, age, gender or hours of TV viewing, to answer a question or interrogate an assertion. The choice of attribute leads to choices of measures for that attribute, for example measure exercise by both time in minutes and intensity using a 1-10 self-reported scale.
At Level Five students sophistication in data collection and analysis should extend to the need for representative sampling and adequate sample size, avoidance of bias in surveys and sampling techniques,  systematic collection and processing of data that does not narrow potential responses, and appropriate use of technology to sort and display data.
Students should use a variety of displays to find patterns or relationships in multivariate data sets. This range of displays should extend to using measures of centrality and spread such as mean or median, range and quartiles. This means that displays such as box and whisker plots and histograms are accessible.

Students should analyse the data by comparing distributions visually using multiple graph types, preferably generated by technology. They should use informal inference to look for differences between distributions, for example, the median of one group is higher than the upper quartile of the other. Students should choose the most appropriate data display to report their findings and draw conclusions from the data related to their investigative question. They should recognise that all findings from the analysis of samples must be interpreted with uncertainty and be cautious in generalizing the results to whole.