# Systematic Sampling: Definition, Examples, Repeated

Probability and Statistics > Sampling > How to Perform Systematic Sampling

## Systematic Sampling: Overview

One way to get a fair and random sample is to assign a number to every population member and then choose the nth member from that population. For example, you could choose every 10th member, or every 100th member. This method of choosing the nth member is called systematic sampling.

Watch the video for an overview and steps:

When you’re sampling from a population, you want to make sure you’re getting a fair representation of that population. Otherwise, your statistics will be biased or skewed and perhaps meaningless.

Systematic sampling is quick and convenient when you have a complete list of the members of your population (for example, this one of the members of Congress). However, if there’s some kind of pattern to the original list, then bias may creep in to your statistics.

For example, if a list of people is ordered as MFMFMFMF, then choosing every 10th number will give you a sample consisting entirely of females. You could randomly shuffle the list before choosing the nth item or you could use repeated systematic sampling, where you take several small samples from the same population. It’s used if you aren’t sure you have a completely random list and you want to avoid sample bias.

### How to Perform Systematic Sampling: Steps

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Step 1: Assign a number to every element in your population. For this simple example, let’s say you have a population of 100 people, so you’ll assign the numbers 1 to 100 to the group.

Step 2: Decide how large your sample size should be. See: Sample size (how to find one). For this example, let’s say you need a sample of 10 people.

Step 3: Divide the population by your sample size. For this example, your population is 100 and your sample size is 10, so:
100 / 10 = 10
This is your “nth” sampling digit (i.e. you’ll choose every 10th item)

• 1 2 3 4 5 6 7 8 9 10
• 11 12 13 14 15 16 17 18 19 20
• 21 22 23 24 25 26 27 28 29 30
• 31 32 33 34 35 36 37 38 39 40
• 41 42 43 44 45 46 47 48 49 50
• 51 52 53 54 55 56 57 58 59 60
• 61 62 63 64 65 66 67 68 69 70
• 71 72 73 74 75 76 77 78 79 80
• 81 82 83 84 85 86 87 88 89 90
• 91 92 93 94 95 96 97 98 99 100

That’s how to perform systematic sampling!

## Repeated Systematic Sampling

The first three steps are exactly the same:

Step 1: Assign a number to every element in your population.

Step 2: Decide how large your sample size should be. See: Sample size (How to find one).

Step 3: Divide the population by your sample size. For example, if your population is 100 and your sample size is 10, then:

100 / 10 = 10

This is your “nth” sampling digit (i.e. you’ll choose every 10th item)

The main difference is that you’ll stop part way through the sampling and switch. Follow the steps to see how this is done:

## Sampling from Group 1

Step 4: Use the sampling digit from Step 3 up to a certain point. This is usually a judgment call; Exactly where you stop is usually quite arbitrary. The goal is to divide your population into parts. For this example, we’ll sample up to 50; By stopping at 50 we are splitting the entire group into two sections.

First, you’ll sample from the first half of the group (in Step 5, you’ll sample from the remainder).

• 1 2 3 4 5 6 7 8 9 10
• 11 12 13 14 15 16 17 18 19 20
• 21 22 23 24 25 26 27 28 29 30
• 31 32 33 34 35 36 37 38 39 40
• 41 42 43 44 45 46 47 48 49 50
• 51 52 53 54 55 56 57 58 59 60
• 61 62 63 64 65 66 67 68 69 70
• 71 72 73 74 75 76 77 78 79 80
• 81 82 83 84 85 86 87 88 89 90
• 91 92 93 94 95 96 97 98 99 100

## Systematic Sampling from Group 2

Step 5: Switch to a different starting point and then continue sampling with the nth digit. Again, this is usually a judgment call. For this example, we’ll switch from 50 to 51.

• 1 2 3 4 5 6 7 8 9 10
• 11 12 13 14 15 16 17 18 19 20
• 21 22 23 24 25 26 27 28 29 30
• 31 32 33 34 35 36 37 38 39 40
• 41 42 43 44 45 46 47 48 49 50
• 51 52 53 54 55 56 57 58 59 60
• 61 62 63 64 65 66 67 68 69 70
• 71 72 73 74 75 76 77 78 79 80
• 81 82 83 84 85 86 87 88 89 90
• 91 92 93 94 95 96 97 98 99 100

Note that we only have 9 in our sample (we wanted 10), so return to the beginning of the list and continue:
1 2 3 4 5 6 7 8 9 10

That’s How to Perform Repeated Systematic Sampling!

## References

Ken Black (2004). Business Statistics for Contemporary Decision Making (Fourth (Wiley Student Edition for India) ed.). Wiley-India.