Question Video: Understanding Biased and Unbiased Samples | Nagwa Question Video: Understanding Biased and Unbiased Samples | Nagwa

Question Video: Understanding Biased and Unbiased Samples Mathematics • Third Year of Preparatory School

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The government wants to conduct a survey about the number of people in the town who think that a park needs to be remodeled. Their plan is to ask a random sample of the park’s visitors to fill in a questionnaire. Which of the following would most likely be the reason the sample is biased? [A] The visitors will not want to spend time filling in the questionnaire. [B] We do not know how they will ensure that the sample is random. [C] There might be a high proportion of children in the sample, which will skew the result. [D] The number of visitors in the chosen sample is not large enough. [E] The park visitors would be more interested in remodeling the park.

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Video Transcript

The government wants to conduct a survey about the number of people in the town who think that a park needs to be remodeled. Their plan is to ask a random sample of the park’s visitors to fill in a questionnaire. Which of the following would most likely be the reason the sample is biased? Option (A) the visitors will not want to spend time filling in the questionnaire. Option (B) we do not know how they will ensure that the sample is random. Option (C) there might be a high proportion of children in the sample, which will skew the result. Option (D) the number of visitors in the chosen sample is not large enough. Or option (E) the park visitors would be more interested in remodeling the park.

In this problem, we are asked for the reason that this sample is biased. So let’s recall that a biased sample is a method of forming a sample which favors certain values of the variable of study. We can consider that the converse of this is a representative or unbiased sample. 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 variable of study here is “Should the park be remodeled?” The population is the people living in the town. The sample is the people who are visiting the park.

And so why is this sample biased? To understand how this will create bias, we need to consider the characteristics of the people who visit the park. These people will hold definite opinions about the park. It could be that they love it or that they think it could be greatly improved. A large number of people not at the park may not hold such strong views, but we do need to include both groups of people in the study. And so there should be a selection from the entire population, not just from the visitors. So, let’s explore the options we were given to find the best reason.

Option (A) deals with the problem that the visitors might not want to spend time filling in the questionnaire. And while this might be particularly true about the visitors to the park, it could be said about any sample group. Even if a random sample of the town was given questionnaires, there will always be a problem with this. But this is more of a problem with the method of data collection, but not the representation of the sample.

Next, let’s look at option (B), which states we do not know how they will ensure that the sample is random. But even if the government does randomly select visitors, the problem is that they are selecting from a restricted population. They are only sampling from the visitors to the park and not from the entire town, which is the population. And the statement here does not address this problem.

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

Next, option (D) which is that the number of visitors in the chosen sample is not large enough. This may be a very valid concern. Generally, if the sample is larger, then the representation is better. In fact, in an ideal world, we would ask the opinions of everyone in the population. However, time and money means that this is usually not a practical option. However, this statement does not address the bias which comes from the fact that it is only the park visitors who are asked.

Finally, option (E) the park visitors would be more interested in remodeling the park. This will be our answer because it addresses the bias that comes from the fact that this method favors certain values of the variable of study. As an aside, one way we could get a representative sample in this situation would be to obtain a list of names and addresses of the people or adults living in the town, number them, and then randomly generate a list of people to mail questionnaires to. Alternatively, telephone interviews could be conducted. This would give us an unbiased sample of the entire population.

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