Question Video: Determining Whether a Particular Definition of a Sample Is True or False Mathematics

True or false: A sample consists of one or more observations drawn from the population.

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Video Transcript

True or false: A sample consists of one or more observations drawn from the population.

To determine whether this statement is true or false, let’s look at how we define the terms in this statement. Let’s first define the population. This is the complete group of people or objects that are the target of a statistical study. Examples might include all of the high school students in a particular country, all of the video games available for a particular games console, all the known genetic variations of rice, of which, according to the International Rice Research Institute, there are 132,000.

We define a sample as a smaller group of individuals or a single individual, in fact, selected from a population. And referring to our examples, a sample of our high school students could involve random selection of five students, for example, from each school. For our video games example, we might select 25 games randomly from the complete list of games. And in our rice variations example, we might select a small number of species from each rice growing country.

Now, in a statistical study, data is collected from either a population or sample in the form of observations. These are facts or figures on a particular variable which are recorded for each sample or population member. And in each of our sample examples, we select a group from the population, noting that in theory a group could consist of one element. And we collect observations on that group. We can therefore say that the given statement, “a sample consists of one or more observations drawn from the population,” is true.

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