4.1 Populations, samples and data collectionIB Maths: Analysis and Approaches SL: Flashcards

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What is a random sample?

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What is a random sample?: A sample in which every member of the population has an equal chance of being chosen.
Discrete or continuous: number of goals scored?: Discrete (counted).
Discrete or continuous: time to run 100 m?: Continuous (measured).
What is a sampling frame?: A list of all members of the population, needed for simple random sampling.
How is a systematic sample taken?: Choose a random start, then every $k$ th item from an ordered list, $k = \frac{N}{n}$ .
Stratified sample of 50 from 400 boys and 600 girls: how many girls?: $\frac{600}{1000} \times 50 = 30$
Difference between stratified and quota sampling?: Stratified chooses randomly within each group; quota does not.
Main weakness of convenience sampling?: It is likely to be biased, because the easiest people to reach may not represent the population.
Outlier rule?: More than $1.5 \times \text{IQR}$ below $Q_1$ or above $Q_3$ .
$Q_1 = 12$ , $Q_3 = 20$ . Is 33 an outlier?: Yes: upper boundary $= 20 + 12 = 32 < 33$ .
Should every outlier be removed?: No. Keep genuine extreme values; remove or correct only errors, giving a reason.
How should missing values be handled when finding a mean?: Leave them out and divide by the number of values actually recorded.
When is stratified sampling most useful?: When the variable is likely to differ between groups in the population.