# Question Video: Understanding Biased and Unbiased Samples Mathematics • 7th Grade

A restaurant owner wants to conduct a survey about whether the residents of a town prefer his restaurant over others or not. His plan is to ask a random sample of the restaurant customers to fill in a questionnaire. Which of the following would most likely be the reason the sample is biased. [A] We do not know how he will ensure the sample is random. [B] The restaurant customers will not want to spend time filling in the questionnaire. [C] The number of customers in the chosen sample is not large enough. [D] The restaurant customers are likely to prefer his restaurant.

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### Video Transcript

A restaurant owner wants to conduct a survey about whether the residents of a town prefer his restaurant over others or not. His plan is to ask a random sample of the restaurant customers to fill in a questionnaire. Which of the following would most likely be the reason the sample is biased. Option (A) we do not know how he will ensure the sample is random. Option (B) the restaurant customers will not want to spend time filling in the questionnaire. Option (C) the number of customers in the chosen sample is not large enough. Or option (D) the restaurant customers are likely to prefer his restaurant.

Here, we are asked why this sample will be 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. 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 relevant to the variable of study. The variable here is the preference of people for this particular restaurant. The population is the people who are resident in the town. The sample is the people who are asked. So that is the restaurant customers.

So for what reason will this sample be biased? To understand how this would create bias, we need to consider the characteristics of the people who are visiting the restaurant. These people will almost certainly be people who firstly prefer the type of cuisine that is being made and secondly who like that particular restaurant. The other people who are not in the restaurant but who are residents in the town might also like the restaurant. For example, they might have been there before.

They might not have tried it before or they might not like it. But the restaurant owner wants responses that are representative of those living in town. He would therefore need to select a sample from everyone, but not simply just from the people that are in the restaurant. And so the best answer is the statement given in option (D). The restaurant customers are likely to prefer his restaurant.

But we can check the other options just to be sure. Option (A), which states that we don’t know how he will ensure the sample is random, may be a valid consideration. But even if the restaurant owner randomly selects visitors, the problem is they’re selecting from this restricted population because they’re sampling only from the customers at the restaurant and not from the entire town, which is the population.

The statement in option (B) regarding the questionnaires could potentially be said about any sample group. Even if a random sample of the town was given questionnaires, there would always potentially be a problem with this. This is more of a problem with the method of data collection, but not the representation of the sample.

In option (C), which states we don’t know if the chosen sample is large enough, may be a valid argument. The larger the sample, the better the representation of the population. But this does not demonstrate our understanding of the bias in the sample which comes from just selecting from the restaurant. And so the answer to which of these statements would most likely be the reason the sample is biased is that given in option (D).