Parameter and statistic
Keep the target population separate from the observed sample
- Parameter A numerical characteristic of the population or model
- Statistic A numerical function of the observed sample
- Sampling variation Repeated samples can give different values of the same statistic
Worked example
A population contains values 1,3,5,7. A selected sample is 1,5. Identify and calculate the two means
\[\mu=\frac{1+3+5+7}{4}=4\]
- \(\displaystyle \overline x=\frac{1+5}{2}=3\)4 is the population parameter; 3 is the realised sample statistic. The statistic does not become a parameter when its value is known
Common mistakes
Known versus unknown
✕a known summary must be a parameter✓classify by the group or model it describes
Both sample statistics and population parameters may be known or unknownDifficulty levels
standardClassify a complete-population summary
examClassify and justify the scope of a census summary
Questions about this topic
Can a known numerical value still be a sample statistic?+
Yes. Its classification depends on whether it describes the selected sample or the target population, not whether it has been calculated
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 11, VCE Units 1 & 2, Specialist Mathematics, chapter 6: Random variables and sampling
In this chapter
Expected value and linear expectation of a discrete random variableVariance, standard deviation and linear variance of a discrete random variableDistribution of a linear transformation of a discrete random variableConstruct finite independent sums and compare repeated copies with scalingDesign and interpret a probability simulationPopulations, samples, parameters, statistics and sampling methodsExact sampling distribution of a sample proportionConstruct sample means and interpret finite sampling distributions