# Question Video: Ensuring the Method of Selection Produces an Unbiased Sample Mathematics • 7th Grade

A school principal wants to find out what the students think about the teaching quality in the school. Which of these samples is unbiased? [A] A list of female students to interview is randomly generated. [B] All ninth grade students are interviewed. [C] A questionnaire is available at the library for anyone who wants to take part in the survey. [D] A list of students to interview is randomly generated. [E] A list of male students to interview is randomly generated.

03:59

### Video Transcript

A school principal wants to find out what the students think about the teaching quality in the school. Which of these samples is unbiased? A list of female students to interview is randomly generated. All ninth grade students are interviewed. A questionnaire is available at the library for anyone who wants to take part in the survey. A list of students to interview is randomly generated. Or a list of male students to interview is randomly generated.

Before we look at each of these options, let’s remind ourselves what it means for a sample to be unbiased. An unbiased sample must be representative of the overall population being studied. Often, time and resource means that we can’t ask every single member of the population. So, if we’re only asking a subsection of them, we must ensure that those people we choose will represent the views of everybody. To ensure this is the case, every member of the population must have an equal chance of being chosen. Let’s now look at the five suggested sampling methods and see which fulfill these criteria.

The first suggested method is that a list of female students to interview is randomly generated. Now, the randomly generated part of this is good. But we can see that only female students are being included in the sample. This means that, assuming the school does have both male and female students, every member of the population does not have an equal chance of being chosen. And so, the views of male students will not be represented in this type of sample. For this reason, then, a list of female students to interview, although it’s randomly generated, would not give an unbiased sample.

In the same way, we can see that the final option was that a list of male students to interview is randomly generated. But this would fail to be an unbiased sample in the same way because this time the views of female students wouldn’t be represented.

What about the second option we were given? Which is that all of the students who were in ninth grade are interviewed. Well, again, this means that every member of the population would not have an equal chance of being chosen. Ninth grade students are certain to be chosen, but students in other grades have a zero probability of being chosen. This sample certainly wouldn’t be unbiased. And it also probably wouldn’t be very good because it’s reasonable to expect that students of different ages may have different opinions on the teaching quality in the school. So, choosing all ninth grade students would not give an unbiased sample.

The third option is that a questionnaire is made available at the library and anyone who wants to take part in the survey can go and fill in the questionnaire. Now, this may seem reasonable because at least the survey is open to everybody this time. But this method of sampling is self-selecting. Only students who choose to participate will be included in the survey. It’s possible that students who visit the library may not be representative of the overall student population. And so, selecting students for inclusion this way would not given an unbiased sample.

The final option is that a list of students to interview is randomly generated. Now, this would give an unbiased sample because every single student in the student population has the same chance of being on this list. We’re told that the list is randomly generated. And so, this method of selection would be representative of the overall population and would be considered an unbiased sample. Our answer, then, is that the only one of the five options which would give an unbiased sample is if a list of students to interview is randomly generated.