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

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

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

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