Display a sample's data, then report its shape, centre and spread, and what it suggests about the population: an estimate, with the sampling method and size stated.
A news story says 'Teens sleep 8 hours a night.' Is that every teen, most teens, or a sample's average? A good report says which, and how the sample was chosen.
A report on a sample describes its distribution, then says what it suggests about the population:
shape: symmetric (balanced about the middle), skewed (a long tail to one side), any clusters, gaps or outliers
centre: the mean and median
spread: the range (highest − lowest)
what it suggests: an estimate for the population, with how the sample was chosen and its size
Data you collect yourself is primary data; data someone else collected (the ABS, a website, a study) is secondary data.
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.
The shape
TryTry it on the board and compare the result with your prediction.
A sample of 40
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Take a random sample of 40. Describe its shape, and read its mean, median and range. Was its shape what you predicted?
Use the board. This ticks when you get there.
InvestigateWork out why it happens, one step at a time.
From data to report
Here is the routine for a report.
Worked exampleBefore each step, say what you think comes next.
Random sample of 20 Year 8s: minutes reading per daySay the sample: method and size.
Shape: most 10 to 30,one outlier at 120Describe the shape.
Median 20,mean 25,range 120−5=115Centre and spread (the outlier pulls the mean up).
Year 8s read about 20 minutes a dayAn estimate for the population, with its limits.
Read Leo's report. Did he measure all 200 students?
A sample of 7 students' sleep: 8.0, 9.5, 10.0, 7.5, 9.0, 8.5, 9.0 hours. What is the median, in hours?
Leo reports on his sample. Click the line where his report goes wrong.
ModifyChange the problem on purpose and see what happens.
Compare and report
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Take a stratified sample of 40 (10 from each year). Describe its shape. Is its mean close to the school's mean?
Use the board. This ticks when you get there.
What is the range of the Year 10 sample, in hours?
PractiseA few on your own, to check you have it.
Describing samples
A sample's values are 4, 6, 6, 7, 9, 10, 14. What is the mean?
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
Your report
Write a short report: the method and size, the shape, the mean, median and range, and what it suggests about how much the school's students sleep. Then compare your estimate with the dashed line.
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Need a hint?
Choose a fair method and a size, then take one sample.
Another hint
Report: the sample, the shape, the centre, the spread, and an estimate for the school.
Choose a fair method and a sample size, and take a sample. Then write your report.
Use the board. This ticks when you get there.
For teachers
Students take samples of a simulated school, describe each sample's shape, centre and spread, compare two samples, and report an estimate with its method and size (AC9M8ST02, node 2). About 40 minutes.
I can describe a sample's shape, centre and spread.
I can compare two samples by their centres and spreads.
I can write a report that gives an estimate for the population and says how the sample was chosen.
Before class
Do the Run board yourself first. Students need mean, median, range and dot plots (Year 7) and sampling methods (last lesson).
The one idea: a report describes the sample (shape, centre, spread) and then estimates the population, naming the method and size. The common mistake is reporting a sample's mean as the population's exact value (Leo's mistake).
The board plots the sample's values (rounded to 0.2 h) and gives the mean, median and range; the dashed line is the school's mean, for checking afterwards. Primary data: collected by the student; secondary: by others (ABS, studies).
Wider: find a secondary source (ABS or a health survey) on teenagers' sleep and compare it with the school sample.
Running the lesson
Predict: ask why the values might bunch up.
Run: ask what the median tells you that the range doesn't.
Investigate: ask Leo how many students he measured.
Modify: ask how far apart the two medians are.
Make: ask what word your estimate needs ('about').
The hard part (on purpose)
Writing 'about' and saying how the sample was chosen. Ask: is this every student, or a sample? How was it picked?
When students get stuck
A student reports only the mean. Ask: How spread out are the values? What shape? Fix: Shape, centre and spread, every time.
A student writes the sample's mean as exact for the school. Ask: Did you measure every student? Fix: Write 'about', and give the method and size.
A student can't describe the shape. Ask: Where do most dots sit? Is one side longer? Fix: Symmetric, or skewed towards the long tail; mention clusters, gaps and outliers.
Stretch and support
Stretch: Take five samples of 40 and write each mean. How much do they vary? (Next lesson investigates this.)
Support: A report frame: 'In a [method] sample of [n], the values were mostly [..]. The median was [..] and the range [..]. So the school's students probably [..].'
Where it leads
This completes AC9M8ST02.
Where it leads: how samples vary (next), and full investigations with samples.
What each step is for
the shape: Committing to the shape of 40 students' sleep shows whether they expect real data to cluster.
a sample of 40: Taking a random sample and reading its dot plot and statistics gives the raw material for a report.
from data to report: Find the centre and spread of a sample; a sample's mean is an estimate, not the population's exact value (Leo); primary and secondary data both need their source.
compare and report: A stratified sample's plot, and two samples side by side, show how to compare centres and spreads in a report.
describing samples: Centre, spread, shape and claims about the population, mixed; treating a sample's mean as exact is the planted slip; sampling methods are the review.
your report: Taking a fair sample and writing a full report shows they can analyse and report on a sample distribution.
Now you can
Describe a sample's shape, centre and spread.
Compare two samples by their centres and spreads.
Write a report that gives an estimate for the population and says how the sample was chosen.