Comparing two populations
Use measures of centre and variability calculated from random samples of two populations to make informal comparative inferences about those populations (e.g. whether words in a Grade 7 science book are generally longer than words in a Grade 4 science book): check that each sample was randomly drawn from the population it is meant to describe and is reasonably representative; weigh the difference between the sample centres against the variability within the samples and against how much centres vary from one random sample to another; and state qualified conclusions ('generally', 'on average', 'probably') rather than claiming every member of one population exceeds every member of the other — recognising that a small difference between two samples may be due to chance alone
Lesson
Set out your lesson
“Comparing two populations means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Tally sheet or simple bar/dot sketch
- A short set of category counts
Extra for the adult
Worked example. Cats 4, dogs 2 — cats have more. The tally and comparison are the proof.
Optional challenge. For Comparing two populations, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Comparing two populations, not mastery.
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Comparing two populations means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Tally sheet or simple bar/dot sketch; A short set of category counts. 1. Say the goal of Comparing two populations in plain words once. 2. Adult tallies one category and sketches a bar or dot plot. 3. Child tallies three small data sets and compares the tallest category. 4. Fresh check: one fresh tally comparison. Record and stop. Done: three correct tallies with a comparison sentence each. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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Secondary
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Secondary supports Comparing two populations. An adult previews and guides; this is a learning page, not a scored quiz.
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Check understanding
- Compare random samples of 20 word lengths from two books (means 6.2 and 4.4 letters, both MADs about 0.9) and conclude that the first book probably uses longer words on average
- Explain why surveying volunteers at one school's sports club cannot support a conclusion that all pupils at that school are fitter than pupils at another school
- Judge that a 1-point difference between two sample medians is not convincing when repeated random samples from one population give medians that vary by about 3 points
“If your child randomly picked 20 words from a Year 7 science book and 20 from a Year 4 science book, could they use the averages and spreads to decide whether the older book generally uses longer words — and explain why they'd say 'probably' rather than 'definitely'?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Data & Statistics
- Age range
- Ages 12–13
Standards