1. 11. Sampling and populations
Cambridge University Press
 G K Powers 2013
Study guide Chapter 11

2. Samples
A population is the entire data set and a sample is part of a population.
Counting techniques are used to list all the possible samples of varying sizes from a known small population.
Population parameter is a measurable characteristic of a population, such as the population mean
Sample statistic is a measurable characteristic of a sample such as the sample mean
HSC Hint – The mean of all the possible samples is equal to the population mean.
Cambridge University Press
 G K Powers 2013

3. The ‘capture–recapture’ technique
Use p to represent the population size.
First sample. Write the number captured as the numerator and p as the denominator of a fraction.
Second sample. Write the number recaptured or tagged as the numerator and the number captured in the second sample as the denominator.
Equate the two fractions in steps 2 and 3.
Solve the equation for p.
HSC Hint – The ‘capture–recapture’ technique is only an estimate of the population size.
Cambridge University Press
 G K Powers 2013

4. Random sampling
Random samples occur when items of the population have an equal chance of being selected.
Random numbers can be generated using a table, a calculator or a spreadsheet.
Use the Ran function in a calculator to generate a random number. For example, typing RanInt#(1,4) generates a random number between 1 and 4.
Use the function Rand or Randbetween in a spreadsheet to generate a random number. For example, typing =RANDBETWEEN(1,4) generates a random number between 1 and 4.
HSC Hint – Random samples may miss a particular group if they are used for large populations.
Cambridge University Press
 G K Powers 2013