Statistics: Statistical investigation
Level 1
AO1: Conduct investigations using the statistical enquiry cycle:
This means students will collect, sort and count data. Students will mostly encounter category data.
This data arises from classifying, for example sorting data into colour categories.
Simple number data generated through measurement with whole units is also manageable.
Students should become familiar with displaying category data using pictographs, set diagrams and bar charts.
Discussion should centre on similarities and differences between categories,
for example “Six more people like hokey-pokey ice cream than vanilla”.
Click to download a PDF of second-tier material relating to Level 1 Statistical Investigations (632KB)
Level 2
AO1: Conduct investigations using the statistical enquiry cycle:
This means students will use the statistical enquiry cycle in their 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 Two 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 may be either
category data or whole number data. Category data arises from classifying and the
interest is in how many of the data items fall in each category (called frequency).
Colour and number of doors are two ways to classify cars that will produce category data.
Whole number data comes from situations where only whole number values are possible, e.g.
how many people live in your house? or from rounding of measures, e.g. how long is your pencil
to the nearest centimetre? The most common graphs for displaying category data are pictographs,
bar, strip and pie graphs. Whole number data can be displayed using dot plots or stem and leaf
graphs. Students should communicate their result through reference to their data displays with an
emphasis on similarity and difference, e.g. boys like outdoor games more than girls..
Click to download a PDF of second-tier material relating to Level 2 Statistical Investigations (584KB)
Level 3
AO1: Conduct investigations using the statistical enquiry cycle:
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, e.g. 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), e.g. what is the usual range in heights for 10 year old students?, comparison questions, e.g. are girls taller than boys?, and relationship questions, e.g. 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.
Click to download a PDF of second-tier material relating to Level 3 Statistical Investigations (171KB)
Level 4
AO1: Plan and conduct investigations using the statistical enquiry cycle:
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 s (include many variables, e.g. 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), e.g. what is the usual range in heights for 10 year old students?, comparison questions, e.g. Are girls taller than boys?, and relationship questions, e.g. do older students go to bed later than younger students? They should be able to decide which variables are important for answering their question, e.g. 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, e.g. boys’ heights compared to girls, clusters and outliers within distributions, e.g. middle and spread, associations of variables, e.g. height with armspan, trends over time, e.g. 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.
Click to download a PDF of second-tier material relating to Level 4 Statistical Investigations (185KB)
Level 5
AO1: Plan and conduct surveys and experiments using the statistical enquiry
cycle:
Further detail on this Achievement Objective will be added shortly.
Click to download a PDF of second-tier material relating to Level 5 Statistical Investigations (288KB)
Level 6
AO1: Plan and conduct investigations using the statistical enquiry cycle:
Further detail on this Achievement Objective will be added shortly.
