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Therefore questions like: "How many interviews are needed?" and "How do I select the candidates for the interviews?" must be asked during the design stage of the sampling process.
The most accurate results are obtained if the entire population is sampled for the survey, but this is expensive and time-consuming. The next best method is to randomly select a sample of subjects for the interviews. This means that whatever the method used to select subjects for the interviews, each subject has an equal chance of being selected. There are various methods of doing this for example, names can be picked out of a hat or can be selected by using a random number generator. Most modern scientific calculators have a random number generator or you can find one on a spreadsheet program on a computer.
So, if you had a total population of 1 000 learners in your school and you randomly selected 100, then that would be the sample that is used to conduct your survey.
The remainder of this chapter deals with the mathematical details that are required to analyse the data collected.
The following are some example sets of data which can be used to apply the methods that are being explained.
A fair coin was tossed 100 times and the values on the top face were recorded. The data are recorded in "Data Set 1: Tossing a coin" .
H | T | T | H | H | T | H | H | H | H |
H | H | H | H | T | H | H | T | T | T |
T | T | H | T | T | H | T | H | T | H |
H | H | T | T | H | T | T | H | T | T |
T | H | H | H | T | T | H | T | T | H |
H | T | T | T | T | H | T | T | H | H |
T | T | H | T | T | H | T | T | H | T |
H | T | T | H | T | T | T | T | H | T |
T | H | T | T | H | H | H | T | H | T |
T | T | T | H | H | T | T | T | H | T |
A fair die was cast 100 times and the values on the top face were recorded. The data are recorded in "Data Set 2: Casting a die" .
3 | 5 | 3 | 6 | 2 | 6 | 6 | 5 | 5 | 6 | 6 | 4 | 2 | 1 | 5 | 3 | 2 | 4 | 5 | 4 |
1 | 4 | 3 | 2 | 6 | 6 | 4 | 6 | 2 | 6 | 5 | 1 | 5 | 1 | 2 | 4 | 4 | 2 | 4 | 4 |
4 | 2 | 6 | 4 | 5 | 4 | 3 | 5 | 5 | 4 | 6 | 1 | 1 | 4 | 6 | 6 | 4 | 5 | 3 | 5 |
2 | 6 | 3 | 2 | 4 | 5 | 3 | 2 | 2 | 6 | 3 | 4 | 3 | 2 | 6 | 4 | 5 | 2 | 1 | 5 |
5 | 4 | 1 | 3 | 1 | 3 | 5 | 1 | 3 | 6 | 5 | 3 | 4 | 3 | 4 | 5 | 1 | 2 | 1 | 2 |
1 | 3 | 2 | 3 | 6 | 3 | 1 | 6 | 3 | 6 | 6 | 1 | 4 | 5 | 2 | 2 | 6 | 3 | 5 | 3 |
1 | 1 | 6 | 4 | 5 | 1 | 6 | 5 | 3 | 2 | 6 | 2 | 3 | 2 | 5 | 6 | 3 | 5 | 5 | 6 |
2 | 6 | 6 | 3 | 5 | 4 | 1 | 4 | 5 | 1 | 4 | 1 | 3 | 4 | 3 | 6 | 2 | 4 | 3 | 6 |
6 | 1 | 1 | 2 | 4 | 5 | 2 | 5 | 3 | 4 | 3 | 4 | 5 | 3 | 3 | 3 | 1 | 1 | 4 | 3 |
5 | 2 | 1 | 4 | 2 | 5 | 2 | 2 | 1 | 5 | 4 | 5 | 1 | 5 | 3 | 2 | 2 | 5 | 1 | 1 |
There are regulations in South Africa related to bread production to protect consumers. Here is an excerpt from a report about the legislation:
"The Trade Metrology Act requires that if a loaf of bread is not labelled, it must weigh 800g, with the leeway of five percent under or 10 percent over. However, an average of 10 loaves must be an exact match to the mass stipulated. - Sunday Tribune of 10 October 2004 on page 10"
We can use measurements to test if consumers getting value for money. An unlabelled loaf of bread should weigh 800g. The masses of 10 different loaves of bread were measured at a store for 1 week. The data are shown in [link] .
Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
802.39 | 787.78 | 815.74 | 807.41 | 801.48 | 786.59 | 799.01 |
796.76 | 798.93 | 809.68 | 798.72 | 818.26 | 789.08 | 805.99 |
802.50 | 793.63 | 785.37 | 809.30 | 787.65 | 801.45 | 799.35 |
819.59 | 812.62 | 809.05 | 791.13 | 805.28 | 817.76 | 801.01 |
801.21 | 795.86 | 795.21 | 820.39 | 806.64 | 819.54 | 796.67 |
789.00 | 796.33 | 787.87 | 799.84 | 789.45 | 802.05 | 802.20 |
788.99 | 797.72 | 776.71 | 790.69 | 803.16 | 801.24 | 807.32 |
808.80 | 780.38 | 812.61 | 801.82 | 784.68 | 792.19 | 809.80 |
802.37 | 790.83 | 792.43 | 789.24 | 815.63 | 799.35 | 791.23 |
796.20 | 817.57 | 799.05 | 825.96 | 807.89 | 806.65 | 780.23 |
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