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

Liam wants to find out the proportion of seventh-grade students who have already been abroad. There are 250 seventh-grade students in his school. He decides to number all of them from 1 to 250, generate a random list of 40 numbers between 1 and 250, and then interview the corresponding students. Is his sample biased?

02:00

### Video Transcript

Liam wants to find out the proportion of seventh-grade students who have already been abroad. There are 250 seventh-grade students in his school. He decides to number all of them from one to 250, generate a random list of 40 numbers between one and 250, and then interview the corresponding students. Is his sample biased?

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 whether a student has been abroad. The population in Liam’s study is seventh-grade students. And so his sample is of seventh-grade students. If the population was the whole school, then just sampling the seventh grade would lead to a biased study. However, he takes a sample of 40 from the entire population; that’s the 250 seventh-grade students.

We can note that Liam chooses a random sample of students because he numbers them all from one to 250 and generates a random list of 40 numbers. These 40 numbers correspond to random students. The random sample of students gives each student an equal chance of being in the sample. And this will lead to a representative sample. Because the sample comes from an unbiased sampling method, then the sample is unbiased. And so to answer the question “Is his sample biased?,” then we could give the answer no.

An example of a biased sample in this context might be Liam asking his friends or certain groups within the seventh grade, for example, his math class or members of clubs, such as the chess club or the gymnastics team. But because the sample here was randomly generated, then there was no bias.