Estimating from a sample
Use data from a random sample to estimate a characteristic of the population, such as a proportion, total count, or mean; present the result as an estimate rather than an exact population measurement; state the assumptions the inference relies on (the sample was randomly drawn from the population being described and is reasonably representative) and explain how the conclusion is limited or invalid when those assumptions fail
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Estimating from a sample 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 Estimating from a sample 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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Start practiceEstimating from a sample practice
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Secondary
Before you open · source notes
Secondary supports Estimating from a sample. An adult previews and guides; this is a learning page, not a scored quiz.
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Before you openAsk the learner one fact they learned and one question they still have.
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Source, access and review notes
Public NRICH page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
NRICH. “Secondary.” External page; Gakuva does not copy, host, embed, or redistribute materials.
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Check understanding
- Use a sample proportion to estimate a population count — e.g. 18 of a random sample of 60 pupils walk to school, so estimate about 270 of the school's 900 pupils walk — and state the answer as an approximate estimate rather than an exact count
- Use the mean of a random sample (e.g. the mean weekly reading time of 25 randomly chosen pupils) to estimate the population mean, and explain why the true population mean is likely to be close to, but probably not exactly equal to, the sample mean
- State the assumptions behind an estimate and explain why it becomes unreliable or invalid when they fail — e.g. using a sample of only Year 7 pupils to estimate for the whole school, or using a volunteer online poll — and identify what can and cannot be concluded from the data
“If your child learns that 12 out of 40 randomly chosen pupils at their school play an instrument, could they estimate how many of the school's 600 pupils play one — and explain why that number is a sensible estimate rather than an exact count?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Data & Statistics
- Age range
- Ages 12–13
Standards