# Lesson Video: Sample and Population Methods Mathematics

In this video, we will learn how to determine when to take a sample and when to use the whole population.

08:15

### Video Transcript

In this video, we will learn how to determine when to choose between taking a sample and using the whole population. We will begin by defining what we mean by these terms when dealing with statistics. The study of statistics revolves around the study of data sets. In this video, we will discuss two important types of data sets, populations and samples. A population includes all of the elements from a set of data. A sample, on the other hand, consists of one or more observations drawn from the population.

Whilst we will not focus on them in this video, there are many different ways of obtaining a sample: for example, random sampling, systematic sampling, and stratified sampling. In this video, we will only be looking at whether we should choose the whole population or a sample of the population. A sample usually has fewer observations than the population. We use a sample due to constraints or an inability to study the whole population. The most common constraints are time and money. However, there are other constraints that could also impact our ability to study the whole population. We will now look at some specific questions in context.

Which of the following data sets would be suitable to check the education level in the poor villages in Africa? Is it (A) mass population or (B) samples?

When deciding which data set to use, we need to factor in any constraints. Two of the biggest constraints when collecting data are time and money. In this particular question, we need to ask ourselves whether it is possible to check the education level of every child in the poor villages in Africa. If this was a sensible method, we could use the mass population. However, as it is not realistic to visit every village in Africa, we need to choose samples.

We could choose a sample of different villages and then a sample of children from each of the villages chosen. This would be the most suitable way to check the education level in the villages in Africa.

Which of the following data sets is suitable to calculate how many hospitals there are in a city? Is it (A) mass population or (B) samples?

When deciding which type of data set to choose, we need to consider any constraints. These include time and money, but they also include what we are trying to find out from our question. In this question, we need to calculate the number of hospitals in a city. This means that we want an exact answer. As a result, taking a sample would not be beneficial, as there could be more hospitals in some areas of the city than in others. In order to calculate how many hospitals are in a city, we would need to count each individual hospital. This means that we need to use the whole population. The correct answer is therefore option (A). The data set that is most suitable is mass population.

In the next two questions, we need to identify whether the data collected is a population characteristic or a sample statistic.

Olivia knows all the families living in her area quite well. She says that she has found out that the average number of children per family is 2.3. Is this figure a sample statistic or a population characteristic?

We recall that a population includes all the elements from a data set. A sample, on the other hand, consists of one or more observations drawn from the population. The keyword in this question is “all” as it states that Olivia knows all the families in her area. She has found out the average number of children per family using the entire population of her area. The correct answer is therefore a population characteristic.

A study claims that 96 percent of people aged 16 to 24 in a certain country own a smart phone. Is this a sample statistic or a population characteristic?

We recall that a population includes all the elements from a data set. In this question, this would be all the people aged 16 to 24 in a country. A sample, on the other hand, consists of one or more observations drawn from the population. Due to the constraints of time and money, it would be very difficult to ask every 16- to 24-year-old in a country. Typically, this would only happen when conducting a census. This means that the 96 percent that the study claims must be based on a sample of the population. The correct answer is therefore a sample statistic.

Any study of this type will not be able to ask the entire population but instead will focus on a sample. This sample could have been obtained using a variety of methods. Random sampling, systematic sampling, or stratified sampling are examples of this.

In our final example, we will identify some keywords involved in sampling.

Which of these makes an inference in statistics? Is it (A) computing a statistic from the sample? (B) Generating a random sample from a given population. (C) Applying conclusions drawn from a sample of a whole population. Or (D) working out the percentage of the population that exhibits a certain characteristic.

Statistical inference is the process of using data analysis to deduce properties of a population. This means that we’re looking to make conclusions from a sample that could apply to the whole population. The correct answer is therefore option (C). An inference applies conclusions drawn from a sample of a whole population.

We will now summarize the key points from this video. We found out in this video that a population contains all elements of a data set. As a sample consists of one or more observations from the population, it is a subset of the population. This can be shown in the given diagram where the sample is a selection from the larger group or population. All elements of the sample must be contained within the population. We also found out that we can analyze a sample to infer properties of an entire population. This allows us to make further hypotheses or conclusions without asking the entire population.