Video Transcript
What is a population? Option (A) the population is the
numerical data that is being collected in a study. Option (B) the population only
describes the people that are being studied. Option (C) the population is the
part of the set that is being studied. It is a subset of the people,
plants, animals, objects, and so on. Or option (D) the population is the
complete set that is being studied. It can be anything: people, plants,
animals, objects, and so on.
We’re given four options, and we
need to determine which of these options describes a population. So let’s begin by reminding
ourselves of the definition of a population.
We define a population as the
entire set of objects we’re analyzing. It may not be feasible or
cost-effective to analyze data collected from or about the whole population. So, in many cases, we would select
a sample from the population and analyze data from the sample. We define a sample as a smaller
subset of the population. And samples are a great way of
obtaining information quickly. For example, it’s much easier and
quicker to ask a sample of 20 students their lunch preferences than it is to ask the
whole school.
So, now we have our definition for
a population, let’s look at our options to see if they fit with our definition of a
population.
Starting with option (A), this
claims that a population is the numerical data that is being collected in a
study. In fact, this is not true. We collect data on the members of a
population. For example, if our population is
the students in a school, we might collect data on the students’ grades. We might also collect data on the
students’ shoe sizes. We can collect all sorts of data on
the students, but they, the students, are the population. The data collected is not the
population. So we can eliminate option (A). The population is not the numerical
data collected.
Option (B) states that the
population only describes the people that are being studied. In fact, a population can be any
group of objects that we’re interested in studying. It doesn’t necessarily need to be
people. For example, we might want to study
all the trees in a particular forest or all the breakfast cereals sold by a
supermarket. The trees and the breakfast cereals
would then be our populations. So we can eliminate option (B),
since populations aren’t necessarily people.
Option (C) states that the
population is the part of the set that is being studied and is a subset of the
people, plants, and so on. But we see from our definition that
a population is the entire set of objects we’re analyzing. Instead, we see that a subset or
selection of the population is actually a sample. So option (C) describes a sample,
not a population. Hence, we can eliminate option
(C).
Finally, considering option (D),
this says that the population is the complete set that is being studied and that it
can be anything: people, plants, and so on. And we see that this does in fact
match with our definition of a population. It’s the entire set of objects
we’re analyzing. Our answer is therefore option
(D). The population is the complete set
that is being studied, which in fact can be anything.
