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.
