Systematic Random Samples

Systematic Random Samples

Author: Sophia Tutorial

This lesson will explain systematic random sampling.

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What's Covered

This tutorial is going to cover systematic sampling by contrasting simple random sample with:

  1. Systematic Sampling


There is one thing to know about systematic sampling right off the bat: it is not inherently random. You have to be really careful about this. A systematic sample involves assigning a value, k, to individuals within a population. Then, you state that every “k-th” individual is chosen. Kind of like in elementary school when you counted off by 3’s to create teams.

The value of "k" can be anything. You could choose every second individual, in which case all the green people are in, and all these black stick figures are out. Or you could do every third person, where one person is in and then skip two. And then fourth person is in and skip two. Or we could go every fourth person. Make sense so far?

Term to Know

    • Systematic Random Sample
    • A sampling method where every "k"th individual is selected for the sample (e.g. every 2nd, 4th, 20th individual).

Often people prefer systematic samples to simple random sample because systematic samples are so much easier to take. It's easier than getting a whole list of people and assigning everyone a number or putting all the people's names in a hat. It's easier to just take every fifth person or whatever you decide "k" should be.

The nice thing about a systematic sample is that it can be tailored to fit your sample size. If you wanted a sample of 25 from 500 individuals, you could sample every 20th person, and you would obtain your sample of 25.


Suppose that you have 20 students in a class, and they're in rows, assigned to their desks randomly. If that were the case, you could count off every fourth student and have five students go up to the chalkboard to do a homework problem on the chalkboard.

So, person one, two, and three don't have to do it. Person number four heads up to the chalkboard to work on a problem. Five, six, and seven don't have to do it, but number eight does. You can see the checkmarks to indicate the pattern and who needs to go up to the chalkboard.

Think About It
Now, there is a risk if they weren't randomly assigned. What if they were alphabetized instead of randomly assigned?

By selecting say, Adamson, you automatically know who all the rest of the people are going to be. Since Adler is right next to Adamson, you know that Adler won't get chosen. Nor will Anderson or Bueller, but Frye will.

If these students were randomly assigned to the seats, picking Adamson would not predetermine who all the other people were going to be selected for the sample, but having them alphabetized impacts the random selection process.


A simple random sample is the ideal sampling method. However, a systematic sample can be similarly valid, and it's much easier to perform. It involves taking every k-th individual, but the population must be randomly sorted before the systematic selection. Otherwise, it won't be considered random.

Good luck!

Source: This work is adapted from Sophia author Jonathan Osters.

Terms to Know
Systematic Random Sample

A sampling method where every "k"th individual is selected for the sample (e.g. every 2nd, 4th, 20th individual)