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For a school project, three students need to produce a sample of students at their school.
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Which of the following methods leads to a random sample?
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Option A, calling for volunteers at the school assembly.
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Option B, calling for volunteers via social media.
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Option C, writing the names of all students they know in a list.
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Option D, asking each of their friends to name three further friends.
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Option E, numbering all the students and produce the sample from a random list of numbers.
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In this question, we’re asked about a sample of students at a school.
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Taking a sample or sampling in this context refers to taking a subset of the population to estimate the characteristics of that population.
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In order to create a good and a useful sample, it’s very important that it is random.
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If the sample isn’t random, then it will be biased.
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In order to get a random sample from a population such as students at a school, we could start by assigning numbers to all of the population.
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In this case, the students at the school.
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And then, we would use random numbers — for example, randomly generated — to list as many students as we need for the sample.
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Looking at our options, and it appears as if option E would fit this criteria.
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Here, there’re three students would number all the students and then produce the sample from a random list of numbers.
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But let’s have a look at the other options and see if they would also lead to a random sample.
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And if not, then why not?
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Starting with option A which says calling for volunteers at the school assembly.
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It initially looks like a good option because at the school assembly, we would have almost all of the population of school attending.
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However, thinking by the aspect of calling for volunteers, we need to think about the characteristics of the sort of students who will volunteer.
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In this case, we may introduce a bias into the sample.
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For example, if the school project was looking at personalities, then those who have volunteered for the sample will already be displaying particular personality traits, giving a biased sample.
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Additionally, if in the school assembly the students were made aware of the nature of the school project, then this may attract those who have very strong opinions on the topic.
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Because of both of these aspects, the volunteers are not randomly selected.
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So option A doesn’t give a random sample.
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In option B, we have the same problems associated with calling for volunteers, as we saw in option A.
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But we also have the fact that social media is being gazed.
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In this case, the population is limited to those who are using technology.
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Not only does it create a bias, but it also means that the whole population is not being sampled from.
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This means that option B would not produce a random sample.
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Looking at option C then, we have our three students writing the names of all the students they know in a list.
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We know that this will be a biased sample since friendship groups often tend to share similar likes, dislikes, and personality traits.
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Writing the names of people that we know is not creating a random sample.
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Option D is similar to option C in that these three students are potentially asking the friends of their friends to form the sample.
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This is not a randomly generated sample and would be biased.
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Therefore, the answer is not option D.
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Looking again at option E, numbering all the students and producing the sample from a random list of numbers is the best way to produce a random sample in this context.
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And it will be our final answer.