WJEC Maths for AS: Applied sample

1.4 Selecting or critiquing sampling techniques 13 Systematic sampling Advantages • More straight-forward compared to simple random sampling. • Sample is easy to select. Disadvantages • Less random than simple random sampling. Opportunity sampling Advantages • Easy to take the sample as it is drawn from that part of the population that is close at hand. Disadvantages • Sample can be highly unrepresentative of the population as the sample is not picked at random. Example 1 A researcher is collecting data about the amount of television watched by 20 different ϐive year olds on a Saturday. The results in hours are listed below: 1, 10, 2, 5, 8, 0, 1, 1, 3, 2, 9, 9, 12, 5, 1, 2, 4, 9, 7, 12 (a) Taking an opportunity sample of the ϐirst 5 numbers in the list, calculate the mean number of hours watched on a Saturday. (b) A systematic sample is to be taken of 5 data values. (i) Work out the sampling interval. (ii) A random number was chosen in the sampling interval and it was 3. Using this value write down the list of data values in the sample. (iii) Using the list from (ii), work out the mean number of hours watched on a Saturday using this sample. (c) State and give reasons which sampling method is likely to give more reliable results. Answer 1 (a) Mean = 1 + 10 + 2 + 5 + 8 5 = 5.2 (b) (i) sampling interval = population sample size = 20 5 = 4 (ii) 2, 1, 9, 1, 7 (iii) Mean = 2 + 1 + 9 + 1 + 7 5 = 4 (c) The systematic sample. As it is a random sample and uses numbers throughout the distribution and not the ϐirst 5 values which may not be typical of the rest. The random number 3 means that you count along to the third value in the list. This is then the ϐirst data item in the sample. Now count along four numbers and this gives the second data value. This is repeated until the 5 data values are obtained.