DS6 – Sampling and Populations

Basic concepts: Recognise that a sample can provide an estimate of a population characteristic Apply counting techniques to list all possible samples Verify that the mean of all possible sample means is equal to the population mean Describe and use the capture–recapture technique Generate random numbers with a table, calculator or spreadsheet Recognise the effect of sample size in estimating the nature of a population

Samples A population is the entire data set and a sample is part of a population. By studying a sample you can generalise about the population. The sample provides an estimate for a particular population characteristic. For this reason, a sample must be large enough to give a good representation of the population, but small enough to be manageable. We can apply counting techniques to list all possible samples of varying sizes from a known (small) population and investigate the mean of the distribution of all these sample means.

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Capture-Recapture The ‘capture–recapture’ technique is used to estimate population size. The technique works by capturing a random sample of the population. This first sample is tagged and then released. At a later time a second sample is captured, and the recaptured or tagged members recorded. The first sample captured divided by the population is approximately proportional to the number recaptured divided by the number in the second sample captured.

The way Biology teaches it… Typical problem: a sample of 100 is captured and tagged, then released. Another sample of 300 is caught, found that 20 are tagged. How many fish are in the lake? total = 100 x 300 20 = 1500 Works well, easier to remember. Works because it finds how many lots of 20 tagged fish (5) then multiplies by how many in each sample (300). first sample second sample number tagged

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8 The capture–recapture technique was used to estimate the number of people with Alzheimer’s disease in the local community. A doctor saw 54 patients with Alzheimer’s disease in one week. One month later she saw 51 patients including 27 of the same patients who had Alzheimer’s disease. Estimate the number of people in the local community with Alzheimer’s disease.

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Random Number Generators Random numbers can be generated using a table, a calculator or a spreadsheet to assist in establishing random samples. Below is an excerpt from a table of random numbers.

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Generating random numbers by calculator On Casio calculators this function key is labelled RAN#. By pressing the calculator produces a random number from 0 to 0.999. You can then multiply by 100 to get a number from 0 to 100 etc. Insight

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Instructions for use Text

Instructions for use Text