Probability and Statistics > Sampling > How to Perform Systematic Sampling

## How to Perform Systematic Sampling: Overview

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. 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**.

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. How to perform systematic sampling without this type of sampling bias? You could randomly shuffle the list before choosing the nth item or you could use **repeated **systematic sampling. **Repeated systematic sampling **is a type of 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

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)

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!*

### How to Perform Systematic Sampling: Repeated Systematic Sampling

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)

Step 4: **Use the sampling digit from Step 3 up to a certain point**. This is usually a judgment call. For this example, we’ll sample up to 50.

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

Step 4: **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 Systematic Sampling: Repeated Systematic Sampling!

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