ACARA v9 CONTENT DESCRIPTION “plan and conduct statistical investigations by posing and refining questions or identifying a problem and collecting relevant data; analyse and interpret the data and communicate findings within the context of the investigation”
Builds on: Critiquing Statistical Claims (AC9M6ST02). Knowing how claims can mislead leads to running your own investigation — one that is fair, clear and honest from question to conclusion.
The investigation cycle
A statistical investigation is a complete process for answering a question with data, and it runs through five connected stages. First you pose a clear question; then you collect relevant data; then you analyse it by organising and summarising; then you interpret what the data shows; and finally you communicate the findings. Each stage feeds the next, and the whole cycle keeps the work focused on the original question. Learning to move through all five stages, rather than jumping straight to a chart or an answer, is what turns a casual guess into a genuine investigation.
The investigation cycle
A statistical investigation runs through five stages, from question to communicating findings.
Step 1: Question \u2014 Pose a clear, answerable question.
Posing the question
Everything starts with a good statistical question, and not every question qualifies. A statistical question asks about a group and expects answers that vary, such as how the students in a class travel to school. A question with a single fixed answer, like a person's age on a given day, is not statistical because there is nothing to collect and compare. A good question is also answerable with data that can actually be gathered, and clear enough that everyone understands what is being asked. Refining a vague question into a sharp, answerable one is the foundation the rest of the investigation is built on.
Posing a good question
A statistical question asks about a group and expects data that varies, not a single fact.
A statistical question expects varied data, not one fixed fact. Pick A, B or C.
Collecting the data
Once the question is set, the next stage is collecting relevant data fairly. This means deciding what to record, asking everyone in the group, and noting each response without leaving any out or favouring a result. A tally chart is a simple way to record data as it comes in, adding a mark in the right category for each response. Collecting carefully matters because the whole investigation rests on the data: if it is gathered unfairly or incompletely, every later stage will be built on a shaky foundation, no matter how neat the chart looks.
Collecting the data
As data arrives, a tally records each response in its category to build up counts.
Recorded 0 of 8 responses \u2014 a tally collects data into counts as it comes in.
Analysing the data
Analysing means organising and summarising the collected data so its pattern becomes visible. Raw responses are hard to read, but counted into categories and drawn as a bar chart, the data tells a clear story: taller bars mean more responses. A bar chart lets you compare categories at a glance and see which is largest or smallest. Other summaries, like totals or the most common response, also belong to this stage. Analysis does not yet say what the result means; it simply arranges the data into a form ready to be read and interpreted.
Analysing the data
Organising counts into a bar chart makes the pattern in the data easy to see.
Press to draw the bars and analyse how the counts compare.
Interpreting the result
Interpreting is the stage where the organised data is read in the context of the original question. If walking has the tallest bar, the interpretation is that most students walk to school. Interpreting also includes working out totals, comparing groups, and noticing what stands out. The key is to stay tied to what the data actually shows and to the question asked, rather than reading in conclusions the data does not support. A careful interpretation turns a chart full of numbers into a clear, honest answer to the question that started the whole investigation.
Interpreting the result
Interpreting means saying what the data shows, in the context of the original question.
Read what the chart tells you. Pick A, B or C.
Communicating findings
The final stage is communicating the findings so that others can understand and trust them. A clear report states the original question, shows the data, usually with a chart, and gives the finding in plain words. Including the data lets readers see the evidence for themselves rather than simply taking the conclusion on trust. Good communication is honest about what was found and does not overstate it. This stage closes the cycle: a question was asked, data was gathered and analysed, an interpretation was made, and now the result is shared clearly with the people who wanted to know.
Communicating findings
The last stage is reporting clearly: the question, the data shown, and what was found.
How should findings be communicated? Pick A, B or C.
Where investigations lead
The five-stage investigation cycle is how statistics works everywhere, from a class survey to national censuses and scientific studies. The same disciplined path, pose a question, collect data fairly, analyse it, interpret it honestly, and communicate clearly, underlies the data that informs decisions in science, government and everyday life. Carrying out a full investigation, rather than just reading someone else's chart, builds the judgement to ask good questions, handle data with care, and tell the truth about what it shows, a skill that matters far beyond the mathematics classroom.
Quick self-check
1. What is the first stage of a statistical investigation?
2. Which of these is a statistical question?
3. In a survey, Walk got 4, Bus got 2, Car got 2. How many were surveyed in total?
4. With Walk 4, Bus 2, Car 2, what does the data show?
5. What should a clear report of the findings include?