Question Video: Understanding Representatives Mathematics • 7th Grade

A student wants to research the amount of pocket money students in his middle school receive. Which of the following would be the best way to get a representative sample of the population? [A] Asking all the students in the library on a Monday lunchtime how much pocket money they receive. [B] Asking a random sample of 50 students from his grade how much pocket money they receive. [C] Asking the teachers of each class how much pocket money they think the students in their class receive. [D] Asking a random sample of 20 students from each grade how much pocket money they receive.

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Video Transcript

Our third question, we’ll look at what we mean by a representative sample.

A student wants to research the amount of pocket money students in his middle school receive. Which of the following would be the best way to get a representative sample of the population? Option (A) asking all the students in the library on a Monday lunchtime how much pocket money they receive. (B) Asking a random sample of 50 students from his grade how much pocket money they receive. (C) Asking the teachers of each class how much pocket money they think the students in their class receive. Or (D) asking a random sample of 20 students from each grade how much pocket money they receive.

As we’re trying to get a representative sample, we want our sample to be unbiased. In order to do this, we ask ourselves a question, does each member of the population have an equal chance of being selected? If our answer to this question is yes, the sample is unbiased. In this question, the population are the students in the middle school. Each of these students needs to have an equal chance of being selected for the sample to be unbiased. The one that is the best representative sample is the one that is closest to this.

In option (A), all the students in the library on a Monday lunchtime are being asked. This is not very representative of the whole school, as the students will have to be in the library on Monday lunchtime. If they’re not there at this time, they will not be in the sample. So, we can rule out option (A). Option (B) talks about a random sample which suggests that it could be representative of the whole population. However, these students are only selected from the student’s grades. This means that any student in a different grade will not be selected. We can, therefore, say that the sample is biased and will therefore not be a good a representation of the population.

It is pretty obvious that option (C) will not get a good representative sample as we’re not asking the students but the teachers. They are also being asked for their opinion as opposed to the actual money that the students receive. An opinion can be skewed by people’s perceptions and is, therefore, biased. Option (D), like option (B), talks about a random sample. The key here is that we are selecting students from each grade. This means that it will give a good representation of the whole population. Students in each grade will have an equal chance of being selected. Therefore, this is the best way to get a representative sample of the students.

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