Systematic Sample: Definition & Example

What Is a Systematic Sample?

Remember in elementary school gym class when your gym teacher chose to select team captains by lining the class up, having them count off up to three (or some other number), and then say every third person was a team captain? Well, this group of team captains was actually a sample of the students in your class selected using systematic sampling.

Often, when gathering information about a certain population, it's easiest to take a portion of that population, called a sample, and observe this smaller group to draw conclusions about the whole population. This is very useful when the population is quite large.

For example, someone may be trying to plan an office party for an office of 2,500 workers, and they want to know what food choices to have at the party. It would be quite a chore to ask all 2,500 people in the office, so the party planner could choose a sample, say 25, of these workers to represent the whole population and ask them their food preferences.

There are many ways to choose a sample from a population. One of those ways is through systematic sampling. When we take a systematic sample of n objects, we list all of the objects in a population in an ordered manner, and we take every k object from our list to be in our sample. Our starting point will be a random number that's less than the number of objects in our sample. Starting here will ensure we're able to get all n objects without running out of objects to choose by reaching the end of the list. To determine k, or our interval size, we divide the entire population by the number of objects we want in our sample. Let's summarize this process in a series of steps.

Systematic Sampling Process Steps

The following steps are taken to get a systematic sample:

Step 1: Make an ordered list of your entire population.

Step 2: Determine your interval size, k, by dividing the number of objects in the entire population by the number of objects you would like in your sample, n.

Step 3: Starting with a random object in the list that falls within the first n objects, take every k object until you have n objects.

For instance, consider our earlier example where we have 2,500 workers in our population, and we want to take a sample of 25 workers. To take a systematic sample, we would make an ordered list of all 2,500 workers. Next, we would determine our interval size by dividing our entire population (2,500) by the number of workers in our sample (25) to get 2,500/25 = 100. This is our interval size. Lastly, starting at a random worker in the first 25 workers, we would take every 100th worker from the list until we had 25 workers.

Systematic Sampling Examples

Let's consider a couple other examples.

1.) Observe the following list of students in a class.

Class Roster

Suppose we want to choose a sample of six students from this class. We see that there are 24 students in the whole class. Thus, we calculate 24/6 = 4, to see that we want to take every fourth student in the list. We start at any of the first six students, say student number two (Amy). Now, we take every fourth student from there, so we would take students 2, 6, 10, 14, 18, and 22. Thus, the students in our sample would be Amy, Sophie, Ralph, Kenny, Pierre, and Crystal.

2.) Let's imagine we have a group of 5,000 dogs that all have arthritis, and we want to see how prevalent joint pain is in that group of dogs. Because observing all 5,000 dogs would be incredibly time consuming, we decide that we will observe a sample of them and generalize our results to the entire population. We decide that it is possible to observe 100 of these dogs, and we will choose this sample systematically. To do this, we would first put all 5,000 dogs in an ordered list. Then starting with one of the first 100 dogs, we would take every 50th dog (5,000/100) to be in our sample.