Systematic Sample Calculator

Select systematic sample units from a population using a random start and interval, with an explicit floor rule for fractional intervals.

The Systematic Sample Calculator selects units from a numbered population using a random start and interval k = N / n. It checks the allowed start range and lists the first ten selected units, or all selected units when n is smaller than ten.

When k is fractional, the page uses floor(r + (i − 1)k) for each selected unit and states that rule with the result.

Enter the whole-number population size N.
Enter a whole-number sample size n no greater than N.
Choose a random start from 1 to ceil(N / n).
Review the interval and first selected unit numbers.

Systematic selection rule

Interval: k = N / n.

Selected unit i: r + (i − 1)k when k is an integer.

When k is fractional, each unit is floor(r + (i − 1)k).

Reading systematic sample units

Start, interval, and selection rule

The valid start range is based on ceil(N / n). The listed sequence is the first ten selections under the displayed rule, or the complete selection when fewer than ten units are sampled.

Statistics tips and best practices

Use a random start chosen independently from the ordered population list.
Check whether the list has a repeating pattern that could line up with the interval.
Use the same unit numbering and order when applying the selection.

Common mistakes to avoid

Choosing a start outside the permitted range.
Using a fractional interval without following the stated floor rule.
Ignoring periodic ordering in the population list.

The page displays a selection sequence from the supplied population size, sample size, and start. It does not inspect a population list or assess the representativeness of the resulting sample.