What Is Statistical Sampling?
Statistical sampling means choosing a subset of a population so you can learn about the whole group. The main probability methods are simple random sampling, systematic sampling, which takes every kth unit, and stratified sampling, which samples each subgroup.
Enter the population size and the sample size. For a random sample the calculator draws distinct ID numbers using a seed so the draw can be repeated; for a systematic sample it gives the interval and a random start; for a stratified sample it allocates the sample to each stratum in proportion to its size. It also reports the sampling fraction and the worst-case margin of error for a proportion with the finite population correction.
Below you will find the formulas, variables, a worked example and answers to common sampling questions.
How to Use the Statistical Sampling Calculator
- Choose a sampling method.
- Enter the population size N and the sample size n.
- For random and systematic samples, keep or change the seed.
- For stratified samples, list each stratum and its size.
Statistical Sampling Formula
Sampling fraction
Systematic interval
Proportionate allocation
Margin of error with finite population correction
Statistical Sampling Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| N | Population size | |
| n | Sample size | |
| k | Systematic sampling interval | ⌊N ÷ n⌋ |
| Nₕ | Size of stratum h | allocation nₕ = n·Nₕ/N |
Statistical Sampling Worked Example
A school of 500 students needs a sample of 25. For systematic sampling k = 500 ÷ 25 = 20; with a random start of 7 you select students 7, 27, 47, and so on. For stratified sampling with year groups of 220, 150 and 130, the proportionate allocation is 11, 7.5 and 6.5, rounded with largest remainders to 11, 8 and 6.
With the example values loaded in the calculator above, the steps are:
- Each of the 500 units has the same chance n/N = 0.05 of being chosen.
- 25 distinct random numbers between 1 and 500 were drawn using seed 2024, so the same seed reproduces the same sample.
- Margin of error (worst case, p = 0.5) = 1.96 × √(0.25 ÷ n) × √((N − n) ÷ (N − 1)) = 19.12 percentage points.
Result: Method = Simple random sample (without replacement); Selected IDs (25) = 3, 7, 44, 80, 81, 142, 181, 221, 231, 235, 240, 260, 292, 326, 329, 333, 343, 352, 356, 399, 406, 449, 454, 464, 500.
How to Read the Sample
The calculator picks IDs using your chosen method and a seed, so the same seed gives the same sample. For a school of 500 students and a sample of 25, the sampling fraction is 25 ÷ 500 = 5%, and systematic sampling uses every 20th student after a random start such as 7.
The margin of error shown assumes a proportion of 0.5, the worst case, and a 95% confidence level. The finite population correction reduces it when the sample is a large share of the population.
Where Statistical Sampling Is Used
Survey planning
Draw a random sample of IDs from a list before you start fieldwork.
Systematic sampling
Find the sampling interval and see which IDs are chosen.
Stratified samples
Split the sample across groups in proportion to their size.
Teaching
Show how different methods pick different samples from the same population.
Common Statistical Sampling Mistakes to Avoid
- A random sample needs a complete list of the population. If the list misses people, the sample is biased.
- Systematic sampling can go wrong if the list has a repeating pattern that matches the interval.
- Stratified sampling works best when the groups differ from each other and are similar inside.
- Record the seed so you can reproduce the sample later.
Statistical Sampling Terms and Definitions
- Sampling frame
- The list of units from which the sample is drawn.
- Stratum
- A subgroup of the population sampled separately.
Statistical Sampling FAQs
What is a simple random sample?
It is a sample in which every member of the population, and every possible group of that size, has the same chance of being chosen.
How do I calculate the sampling interval?
Divide the population size by the sample size. For 500 students and a sample of 25, the interval is 20.
What is stratified sampling?
You split the population into groups, called strata, and sample from each one. Proportional allocation takes a share of each stratum equal to its share of the population.
What is the sampling fraction?
It is the sample size divided by the population size, n ÷ N. A sample of 25 from 500 has a fraction of 0.05, or 5%.