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Year 9AC9M9ST01

Reading Survey Reports Critically

Analyse reports of surveys in digital media and elsewhere for information on how data was obtained to estimate population means and medians. Analyse how different sampling methods can affect the results of surveys and how choice of representation can be used to support a particular point of view.

A reported average is a claim about a whole population made from a sample. How that sample was chosen decides whether to believe it.

Method

Ask how the data was obtained
Method first, number second.
Sample statistics estimate population values
xˉ estimates μ\bar{x} \text{ estimates } \mu
An estimate, never a fact.
Sampling method decides the bias
Convenience and self-selected samples skew predictably.
Representation can push a view
Truncated axes, chosen scales, cherry-picked time ranges.
Mean or median changes the story
Skewed data makes the mean far higher than the median.

Worked example

e.g. A report says the average income in a suburb is $120000. What should you ask?\text{A report says the average income in a suburb is } \$120\,000. \text{ What should you ask?}
  1. Ask which average was used.mean or median?\text{mean or median?}
  2. A mean is dragged upward by a few very high incomes.skewed data\text{skewed data}
  3. Ask how the sample was chosen.random, or convenient?\text{random, or convenient?}
  4. Ask how many people were in it.a small sample varies wildly\text{a small sample varies wildly}
  5. Ask who published it and why.a property agent has an interest\text{a property agent has an interest}
  6. Conclude: the median would describe a typical resident better.

Practice

Name the weakness, then say which direction it pushes the result.

1
A survey at a train station about public transport. Problem?\text{A survey at a train station about public transport. Problem?}
AnswerOnly users are there — it overstates use.\text{Only users are there — it overstates use.}
2
Which average suits skewed income data?\text{Which average suits skewed income data?}
AnswerThe median.\text{The median.}
3
A graph’s axis starts at 90 not 0. Effect?\text{A graph's axis starts at 90 not 0. Effect?}
AnswerSmall differences look large.\text{Small differences look large.}
4
An online poll gets 50 000 responses. Reliable?\text{An online poll gets 50 000 responses. Reliable?}
AnswerNot necessarily — self-selected.\text{Not necessarily — self-selected.}
5
Why report the sample size?\text{Why report the sample size?}
AnswerIt shows how much the estimate can be trusted.\text{It shows how much the estimate can be trusted.}
6
Can a large sample still be biased?\text{Can a large sample still be biased?}
AnswerYes. Size does not cure a bad method.\text{Yes. Size does not cure a bad method.}
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