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.
