Systematic sampling

Systematic sampling selects every k-th unit from a numbered population list after one random starting point, spreading the sample evenly without drawing k separate random numbers.

ByHoang TruongUpdated July 5, 2026

See it move

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A retail chain numbers 900 customer accounts and wants a sample of 45, giving a sampling interval of 900 ÷ 45, or 20. A random start of 7 is drawn, so the sample runs 7, 27, 47, 67, and onward, adding 20 each time until 45 accounts are selected.

Where it fits

TopicFoundations: Data, Populations & SamplingCoreSubjectData Analysis & StatisticsCore

The formula

LaTeX

k = \frac{N}{n}

Variables

$k$: Sampling interval
$N$: Total population size (units)
$n$: Desired sample size (units)

Round k down to a whole number if it does not divide evenly, then draw the random start from 1 to k.

Check yourself

PracticeCORE

A researcher wants a systematic sample of 60 invoices from a population of 1,200 invoices numbered sequentially from 1 to 1,200. She draws a random starting point of 9. What is the number of the fourth invoice selected in her sample?

Select an answer to check your understanding.