Question Video: Understanding Representative Samples | Nagwa Question Video: Understanding Representative Samples | Nagwa

# Question Video: Understanding Representative Samples Mathematics • Third Year of Preparatory School

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An animal rescue center wants to find out if people in its town think more money should be spent on animal welfare. They plan to ask a random sample of their visitors and volunteers to fill in a questionnaire. Why would their sample not be representative of the town’s population?

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### Video Transcript

An animal rescue center wants to find out if people in its town think more money should be spent on animal welfare. They plan to ask a random sample of their visitors and volunteers to fill in a questionnaire. Why would their sample not be representative of the town’s population? Option (A) people will not want to spend time filling in the questionnaire. Option (B) the center’s visitors and volunteers are likely to be supportive of spending on animal welfare. Option (C) we do not know how they will ensure that the sample is random. Or option (D) there might be a high proportion of children in the sample, which will skew the result.

A sample is representative of the population if the sample and the population share similar distributions of characteristics which are relevant to the variable of study. The population here is the people living in the town. The variable is the spending on animal welfare. So why is the sample of people at an animal rescue center not representative?

To understand this, we will really need to consider the characteristics of people who visit and volunteer at the animal shelter. These people will be in general people who like animals. Visitors and volunteers at the animal shelter will be the people who help animals and will be more likely to think that more help and money should be spent on animal welfare. Therefore, the statement that the center’s visitors and volunteers are likely to be supportive of spending on animal welfare will be the best statement.

But let’s have a quick look at some of the other options we were given. The statement in option (A) says that people will not want to spend time filling in the questionnaire. This statement could potentially be said about any sample group. Even if a random sample of the town, which is the population, was given questionnaires, there will always be a problem with this. This is a problem with the method of data collection but not the representation of the sample.

Next, let’s look at option (C), which states that we do not know how they will ensure that the sample is random. Well, even if the rescue center randomly selects from the visitors and volunteers, the problem is that they are selecting from a restricted population, because they’re sampling only from the visitors to the shelter and not from the entire town, which is the population.

Option (D) is very similar because it doesn’t address the problem with the fact that it is only the volunteers and visitors at the shelter who are asked. Regardless of whether the sample is taken from people in the town or, in this scenario, at the shelter, if only adults and children over a certain age should be asked, then measures should be taken to exclude those children who should not be asked.

And so the statement which best describes why this sample is not representative of the town’s population is that given in option (B).

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