Statistical investigation
S3-1: Conduct investigations using the statistical enquiry cycle:
- gathering, sorting, and displaying multivariate category and whole number data and simple time-series data to answer questions;
- identifying patterns and trends in context, within and between data sets;
- communicating findings, using data displays.
The statistical enquiry 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 Three 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 so it should 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? Data displays, including tables and graphs, expected at Level Three are tally charts, frequency tables, pictographs, bar graphs, strip graphs, and pie charts for category data, dot plots and stem and leaf graphs for whole-number data, and simple line graphs for time series data. Students should be able to use computer technology to create these displays to find patterns, including trends over time, in data 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. Supporting teaching resources.
Click to download a PDF of second-tier material relating to Level 3 Statistical Investigations (171KB)
Statistical literacy
S3-2: Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others.
This means students will learn to become critical consumers of statistically based information. This involves critically analysing the choice of display other people have made to convey statistical information. At Level Three students should be able to gain information from all of the displays mentioned in Statistical Investigation, and be aware of the type of data each display is appropriate for and the kind of pattern or relationship that the display is best at communicating. For example, pictographs, and bar graphs highlight difference between frequencies of categories, for example four more students have blue eyes than green, while pie charts and strip graphs highlight proportions, for example the spinner landed on red about one third of the time. Students should link the claims made by others with the appropriateness of the displays used. Supporting teaching resources.
Probability
S3-3: Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary.
This means students will understand that probability is about the chance of outcomes occurring. At Level Three students should recognise that it is not possible to know the exact probability of something occurring in most everyday situations, for example the chance of a day in March being fine. They should understand that trialling must be used to gain information about the situation and that the results of trial samples vary, for example March 2008 is likely to be different from March 2009. Contrived chance events are used to highlight the variation between expected outcomes from models, and experimental outcomes from trialling. Level Three students are expected to use systematic methods such as listing, tree diagrams with equally likely outcomes, or tables to find all the possible outcomes of simple situations such as tossing coins, drawing cards, or rolling dice. They should accept that experimental samples from those situations, for example tossing a coin ten times, vary from one another, and from the proportions expected from a model, that is, most times five heads do not come up. Supporting teaching resources.
Click to download a PDF of second-tier material relating to Level 3 Probability (116KB)