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Ignition Learning — Activity Sheet

Collecting data: census, sampling & experiments

Mathematics · Year 8

Name: ______________________Date: ____________

How you collect data shapes how trustworthy your conclusions are. A census collects data from an entire population — accurate but often expensive or impractical for large groups. Sampling collects data from a smaller, representative subset — faster and cheaper, but only as reliable as how well the sample represents the whole population. An experiment actively tests something under controlled conditions (like trialling a new fertiliser on some plants but not others). Observation records what naturally happens without intervening. Each method has practical trade-offs — a national census is thorough but happens rarely; a quick opinion poll (sampling) is fast but can be skewed by who is asked.

Example

The Australian Census surveys every household in the country (a true census) — hugely accurate but only practical every 5 years. A company wanting quick feedback on a new product instead surveys 200 random customers (sampling) — faster, but the result is only an estimate of what all customers think, not a certainty.

Key terms

Census:
Data collection from an entire population.
Sample:
A smaller, representative subset of a population used to estimate results for the whole.

Questions

  1. 1. A census collects data from:

    • An entire population
    • Just a small sample
    • No one at all
    • Only volunteers
  2. 2. Sampling collects data from:

    • A smaller, representative subset of a population
    • The entire population always
    • Nobody at all
    • Only the researcher
  3. 3. An experiment involves:

    • Actively testing something under controlled conditions
    • Only observing without any intervention
    • Guessing with no data at all
    • Only surveying opinions
  4. 4. Observation means:

    • Recording what naturally happens without intervening
    • Actively changing conditions to test something
    • Surveying only a tiny sample
    • Ignoring all real-world data
  5. 5. The Australian Census aims to survey:

    • Every household in the country
    • Only 100 households
    • Only capital cities
    • No households at all
  6. 6. A key advantage of sampling over a census is that it is generally:

    • Faster and cheaper
    • Always more accurate
    • Legally required everywhere
    • Impossible to do incorrectly
  7. 7. A trial testing a new fertiliser on some plants but not others is an example of:

    • An experiment
    • A census
    • Pure observation with no testing
    • Guessing
  8. 8. Why is a census generally more accurate than sampling, but less practical for large populations?

    • It captures data from everyone, but collecting from an entire large population takes significant time and cost
    • A census is always faster and cheaper than sampling
    • Census data is always less accurate than a sample
    • There is no practical difference between the two methods
  9. 9. A quick opinion poll asking 500 people is an example of:

    • Sampling
    • A full census
    • Pure observation only
    • An uncontrolled experiment
  10. 10. Why might a company prefer sampling over a census when testing customer opinions on a new product?

    • Sampling gets useful results quickly and affordably, even if slightly less precise
    • A census is always faster for a company to conduct
    • Sampling is always illegal for company research
    • There is no benefit to sampling over a census
  11. 11. Recording rainfall data every day without changing anything is an example of:

    • Observation
    • A controlled experiment
    • A census of rainfall
    • Guessing
  12. 12. Why might an experiment (rather than observation) be needed to determine whether a new fertiliser actually causes better plant growth?

    • A controlled test with a comparison group can show cause and effect, not just a correlation
    • Observation always proves cause and effect just as well as an experiment
    • Experiments never reveal anything about cause and effect
    • Fertiliser effects cannot be tested using any method
  13. 13. A national population count that happens only once every 5 years is generally conducted as:

    • A census
    • A daily sample
    • A one-off small experiment
    • Pure observation only
  14. 14. Which data collection method would be most practical for measuring the exact height of every student in a small class of 20?

    • A census (measuring everyone, since the group is small)
    • A large-scale sample of thousands
    • An uncontrolled experiment
    • This cannot be measured at all
  15. 15. Why might the practicalities of a census (cost, time, sheer scale) make sampling the only realistic option for many national surveys?

    • Surveying millions of people directly is often far too expensive and time-consuming to repeat frequently
    • Cost and time are never a real barrier to conducting a census
    • A census is always cheaper than sampling regardless of population size
    • National surveys never face any practical limitations
  16. 16. A researcher wants to know if a new teaching method improves test scores. Why might a controlled experiment (some classes use it, others don't) be more convincing than simply observing scores after everyone uses it?

    • A comparison group makes it possible to isolate whether the method itself caused the improvement
    • Observation alone always definitively proves causation
    • A comparison group provides no additional evidence
    • Controlled experiments are never useful in education research
  17. 17. Why might combining sampling with periodic census data give researchers the best of both approaches over time?

    • Frequent sampling provides regular estimates, while an occasional census provides a highly accurate benchmark to check against
    • Combining methods provides no additional benefit over using just one
    • Census data becomes useless once any sampling has been done
    • Sampling and census data can never be meaningfully compared
  18. 18. Why might purely observational data about smoking and lung disease be less conclusive about causation than a controlled experiment?

    • Ethical and practical barriers mean smoking experiments on humans can't be conducted, so other factors could still explain the observed link
    • Observational data always proves causation as strongly as a controlled experiment
    • There is no meaningful difference between observation and experimentation
    • Correlation and causation always mean exactly the same thing
  19. 19. A retailer wants fast weekly sales trend data, not a perfectly precise once-a-decade count. Which method suits their needs better?

    • Sampling, for frequent, timely (if slightly less precise) insight
    • A full census every week
    • Pure observation with no data recorded
    • Neither method would be useful
  20. 20. A health department wants to know if a new vaccine reduces infection rates. Why would a controlled experiment be preferred over simply observing infection rates in the general population?

    • A controlled experiment with a comparison group can isolate the vaccine's effect from other factors that also influence infection
    • Observation alone always proves the vaccine caused any change
    • Experiments provide no more useful information than observation
    • Health researchers never need to control for other factors
  21. 21. Understanding census, sampling, experiment and observation mainly helps you to:

    • Choose an appropriate, practical data collection method for a given research question
    • Assume every data collection method gives identical results
    • Avoid ever collecting real data
    • Always use a census regardless of the situation

Answer key (parent copy)

  1. 1. An entire population
  2. 2. A smaller, representative subset of a population
  3. 3. Actively testing something under controlled conditions
  4. 4. Recording what naturally happens without intervening
  5. 5. Every household in the country
  6. 6. Faster and cheaper
  7. 7. An experiment
  8. 8. It captures data from everyone, but collecting from an entire large population takes significant time and cost
  9. 9. Sampling
  10. 10. Sampling gets useful results quickly and affordably, even if slightly less precise
  11. 11. Observation
  12. 12. A controlled test with a comparison group can show cause and effect, not just a correlation
  13. 13. A census
  14. 14. A census (measuring everyone, since the group is small)
  15. 15. Surveying millions of people directly is often far too expensive and time-consuming to repeat frequently
  16. 16. A comparison group makes it possible to isolate whether the method itself caused the improvement
  17. 17. Frequent sampling provides regular estimates, while an occasional census provides a highly accurate benchmark to check against
  18. 18. Ethical and practical barriers mean smoking experiments on humans can't be conducted, so other factors could still explain the observed link
  19. 19. Sampling, for frequent, timely (if slightly less precise) insight
  20. 20. A controlled experiment with a comparison group can isolate the vaccine's effect from other factors that also influence infection
  21. 21. Choose an appropriate, practical data collection method for a given research question