Sampling and a large data set
Введено| English | Значение |
|---|---|
| sampling frame/ˈsæmplɪŋ freɪm/ | селекционная рамка |
Who is missing from the data?
- A weather database has a missing entry and several stations. Treating each row as identical can distort a comparison.
- This lesson studies sampling frame 抽样框: The list or population definition from which a sample is selected.
The method
- Identify the population, sampling unit and frame.
- Distinguish random, systematic, stratified, quota and opportunity sampling.
- Missing data is not zero; verify units, dates and variable definitions before comparing samples.
Why does doubling a biased sample not remove the bias?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Bias comes from HOW the sample is chosen, not its size. Surveying twice as many volunteers still over-represents people with strong opinions; only changing the selection method helps.
A worked case
A population has 120 students in one group and 80 in another. A proportional stratified sample of 30 needs 30×120/200=18 from the first and 12 from the second. Random selection is then needed within each group.
Sampling and a large data set
Identify the population, sampling unit and frame
Allocate proportionally, then explain why random selection within each group still matters.
Find the first-group allocation when sample size is 30 and group sizes are 120 and 80.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Allocate 30×120/200=18, then select randomly within that group.
Where it goes wrong
- A large biased sample remains biased.
- Stratification is not the same as selecting whoever is available from each group.
- AQA large-data-set familiarity requires the actual supplied data and metadata, not invented weather values.
Not true: Doubling a biased sample removes its selection bias. A bigger sample collected the same biased way keeps the same bias; only better sampling removes it.
Find the second-group allocation for that sample.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Allocate 30×80/200=12. Check that 18+12=30.
A bigger sample collected the same biased way keeps the same bias.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
True. A bigger sample collected the same biased way keeps the same bias; only better sampling removes it.
Applying it
- For AQA, use the official large data set in a supervised spreadsheet task: identify a variable, justify a comparison, inspect missing values, create a display and explain a limitation.
- Save the decisions with the analysis.
A sample includes 45 of 300 people. Find its percentage.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Percentage=45/300×100=15%.
Match each sampling method to its description.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
The method names describe how members are picked; only probability-based methods support unbiased population claims.
In your course
- AQA A-level Mathematics (7357), specification section K.
- Every paper allows a calculator, but method marks still need the expression or equation written before its value.
- Sampling frame: The list or population definition from which a sample is selected.
- Identify the population, sampling unit and frame.
- Watch for: A large biased sample remains biased.