# Question Video: Understanding Representative Samples Mathematics • 7th Grade

Which of the following is a representative sample? [A] To find out how students travel to school, student representatives from each grade ask a random sample of 20 students from across the grade. [B] A hospital wants to investigate the reasons why people go to the emergency room, so questionnairesare handed out to a random sample of people waiting in the emergency room on a Monday morning. [C] A market research company wants to find out how much waste people recycle, so they survey 100 people at the city recycling drop-off location. [D] A student wants to find out how much students at their school enjoy math classes, so they give a questionnaire to everyone at the math club.

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### Video Transcript

We’ll now look at two further questions in different scenarios.

Which of the following is a representative sample? Is it (A) to find out how students travel to school, student representatives from each grade ask a random sample of 20 students from across the grade. (B) A hospital wants to investigate the reasons why people go to the emergency room, so questionnaires are handed out to a random sample of people waiting in the emergency room on a Monday morning. (C) A market research company wants to find out how much waste people recycle, so they survey 100 people at the city recycling drop-off location. (D) A student wants to find out how much students at their school enjoy math classes, so they give a questionnaire to everyone at the math club.

A representative sample is a subset of the population that seeks to accurately reflect the characteristics of the larger group. This means that, where possible, it needs to be unbiased, such that each member of the population has an equal chance of being selected. In option (A), the population is the students in the school. As they are selecting a random sample of 20 students from each grade, this will represent the whole school. Option (A) is, therefore, a representative sample of the whole school as students are not selected based on gender, age, or interest.

In option (B), the population is the people visiting the hospital’s emergency room. Whilst they are asking people in the emergency room, they’re only asking on Monday mornings. This means that the sample is not representative, as people visiting the emergency room at any other time cannot be selected. In option (C), the market research company wants to look at the whole population to see how much they recycle. As they are only serving people at the city recycling drop-off location, the survey is biased. The results would be skewed as these people are more likely to recycle more waste than the general public. This means that option (C) is not a representative sample.

In option (D), the population is the students in the school. As they are only asking students at math club, the questionnaire will be biased. Once again, this is not a representative sample, as those students at math club are more likely to enjoy math classes. Once again, this will skew the results. The correct answer is option (A).