An investigation asks a question that data can answer, plans who to measure and how, collects and displays the data, describes its shape, centre and spread, and reports an answer with its limits.
Do students your age sleep less on school nights? You could argue about it, or you could measure it. What would you need to decide first?
A statistical investigation goes through these stages:
Ask a statistical question: one that data can answer, with a variable you can measure ("How many hours do Year 7 students sleep on school nights?").
Plan: decide the variable (discrete if counted, continuous if measured), the sample (who, and how many) and how to measure it. Look out for bias, where the sample or the measuring favours one answer.
Collect the data, display it (dot plot, stem-and-leaf plot), and summarise it: shape, centre and spread.
Report an answer to the question, with its limits (who was measured, how many, how).
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Which is a statistical question?
Think: what would you measure, and from whom?
TryTry it on the board and compare the result with your prediction.
Add your own data
Click on the line to add a value.
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The class measured 15 students. Add your own hours of sleep, so there are 16 values.
Use the board. This ticks when you get there.
InvestigateWork out why it happens, one step at a time.
Planning and bias
How is it measured?
Read Kai's working. Who did he ask?
Kai wants to know how long Year 7 students sleep. Click the line where he draws a conclusion he cannot support.
ModifyChange the problem on purpose and see what happens.
Compare and report
Name both the centre and the spread.
Need a hint?
School nights has 7 values; the weekend has 10.
Another hint
Add three values to the school nights.
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Make the comparison fairer by giving school nights as many values as the weekend (10).
Use the board. This ticks when you get there.
PractiseA few on your own, to check you have it.
Investigations
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Hours of sleep: 7, 8, 9. What is the mean?
Review: what is the median of 4, 7, 9, 12, 13?
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
Your investigation
Now write a report of four short parts: the question, the plan (variable, sample and how you would choose it), what the data show (shape, centre, spread), and the limits of your answer.
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Need a hint?
Click the line to add values, or type them in the box.
Another hint
A median of 8.5 needs values on both sides of it.
Build a sample of 20 sleep values whose median is 8.5 hours.
Use the board. This ticks when you get there.
For teachers
Students plan an investigation (question, variable, sample, bias), then summarise and report one in terms of shape, centre and spread (AC9M7ST03, nodes 1 and 2). About 40 minutes.
I can plan a fair sample and name a possible bias.
I can report what data show using shape, centre and spread, and say the limits.
Before class
Do the Run board yourself first. Students need the data lessons before this one (kinds of data, centre, stem-and-leaf plots, comparing data).
The one idea: the answer is only as good as the question and the sample. A small, friendly sample describes that group and not the whole year (Kai's mistake).
This lesson gives the shape of a whole investigation with sleep as the example. The real investigation is a class task: students choose their own question (sleep, screen time, reaction time, jumping), collect data in class, display it on the data board or a spreadsheet and write the report in the four parts of the Make task. Do at least two investigations in different contexts, so the skill transfers.
A public source (the Australian Bureau of Statistics, for example) can give a second set for a social question; use it as an extension.
Running the lesson
Predict: ask what number you would write down for each question.
Run: ask what the new value does to the median and to the range.
Investigate: ask students to name a second source of bias.
Modify: ask what the report would say with different samples.
Make: ask students to swap reports and find the limits the author left out.
The hard part (on purpose)
Planning before collecting. Ask students to say who they would measure and how, before looking at any numbers.
When students get stuck
A student asks an opinion question. Ask: What would you write down for each person? Fix: Turn it into a variable you can measure.
A student generalises from a few friends. Ask: Would your friends be like the rest of Year 7? Fix: Say who was measured, and how they were chosen.
A student reports only the mean. Ask: How spread out are the values? Fix: Report shape, centre and spread.
Stretch and support
Stretch: Repeat the investigation with a sample twice the size. How much do the median and range change? Compare it with a published data set.
Support: Give students the report in four sentence starters: My question was…, I measured…, The data show…, This is limited because…
Where it leads
This completes AC9M7ST03, with a class investigation.
Where it leads: comparing larger data sets, histograms and scatter plots (Year 8).
What each step is for
which is a statistical question?: Committing to which question data can answer shows whether they can tell a measurable variable from an opinion.
add your own data: Adding a value to a collected sample and watching the centre and spread update shows data feeding the summary.
planning and bias: A plan names the variable, its type and a fair sample; one small, friendly sample (Kai) cannot speak for a whole year group.
compare and report: Comparing school nights with weekends uses centre and spread together, needs sets of the same size to be fair, and handles an outlier by checking it first.
investigations: Summaries, variable types and a median review, mixed; calling a small friendly sample the whole group is the planted slip; the median review keeps the centre fresh.
your investigation: Building a data set to a target and writing the report in the four stages puts the whole cycle together.
Now you can
Write a question that data can answer.
Plan a fair sample and name a possible bias.
Report what data show using shape, centre and spread, and say the limits.