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

A student wants to research the number of students in his middle school who ride the school bus. Which of the following is the best method to obtain an unbiased sample?

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Video Transcript

A student wants to research the number of students in his middle school who ride the school bus. Which of the following is the best method to obtain an unbiased sample? Option (A) asking all of the students in the gymnastics team if they ride the school bus. Option (B) asking all of the students in the library on Thursday if they ride the school bus. Option (C) asking a random sample of five students in the hallway if they ride the school bus. Option (D) asking a random sample of 50 students from his grade if they ride the school bus. Or option (E) asking a random sample of 100 students during lunchtime if they ride the school bus.

We can recall that a biased sample is a method of forming a sample which favors certain values of the variable of study. The variable of study here is riding the school bus. We need to determine if there is a representative sample of the population. The population here is the students in the middle school. If there is a representative sample, then each individual in the population, in this case in the middle school, has an equal chance of being selected in the sample. So let’s take a look at each scenario in turn.

In options (A) and (B), the student asks all of the students in, firstly, the gymnastics team or the library on Thursday. In these options, both these groups of people will form part of groupings, which may hold similar characteristics. For example, we might wonder if students in the gymnastics group might be more likely to walk or even cycle to school. For the students in the library, are they perhaps not taking part in a sports activity on Thursday? Perhaps that would also influence how likely they are to take the bus to school. And so we could say that, in each of the options (A) and (B), there may be a bias.

In the next three options, we can see that there is an increasing number of students each time in the sample. The larger the sample, the better. In option (C), the five students are selected from those that are in the hallway. This may help with the randomization, so this is a positive aspect of option (C). But the sample size is quite small.

So let’s see if options (D) or (E) would be better. In option (D), the sample of 50 students is a sample selected from the same grade as the student. The 50 students is a larger number, but the same grade indicates that the students will be the same age. Therefore, there is a bias towards the age, which will affect the outcome of riding a bus. In the final option, we are told that 100 students are selected during a lunchtime. There is an element of randomization in this scenario because the students aren’t selected by age or by activity. This is therefore the best way to get a representative and an unbiased sample.

And so the answer is option (E) asking a random sample of 100 students during lunchtime if they ride the school bus.