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