# S4-1: Plan and conduct investigations using the statistical enquiry cycle: determining appropriate variables and data collection methods; gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends; comparing distributions visually; communicating findings, using appropriate displays.

This means 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:

At Level Four students should be able to pose questions that they want to investigate, consider the appropriate data they need to collect, gather and sort the data in order to develop an answer to their question. The data involved should be multivariate (include many variables, for example gender, age, height, eye colour, bedtime, etc.) so that relationships between the variables can be explored. Students should be able to ask summary questions (of a variable), for example what is the usual range in height for 10-year-old students?, comparison questions, for example are girls taller than boys?, and relationship questions, for example do older students go to bed later than younger students? They should be able to decide which variables are important for answering their question, for example quality of a sports player might be determined by points scored, assists, defensive turnovers or other variables. Students should also consider their methods of data collection, considering issues such as manageability, sampling, surveying, data safety, and technology use. Data displays, including tables and graphs, expected at Level Four are tally charts, frequency tables, pictographs, bar graphs, strip graphs, and pie charts for category data, dot plots, stem and leaf graphs and scatterplots for measurement data, and line graphs for time series data. Students should be able to use computer technology to create these displays to find patterns in the data, including differences and similarities between distributions, for example boys’ heights compared to girls, clusters and outliers within distributions, for example middle and spread, associations of variables, for example height with armspan, trends over time, for example cellphone use over a day, as well as to communicate their findings to others. They should be able to justify their choice of display/s with reference to the patterns they wish to highlight.