Calculator Form
Example Data Table
This example shows a classroom population and a sample of four units.
| Population Index | Population Unit | Possible Selected Status |
|---|---|---|
| 1 | Student 001 | Eligible |
| 2 | Student 002 | Eligible |
| 3 | Student 003 | Eligible |
| 4 | Student 004 | Eligible |
| 5 | Student 005 | Eligible |
| 6 | Student 006 | Eligible |
| 7 | Student 007 | Eligible |
| 8 | Student 008 | Eligible |
Formula Used
Sampling fraction: f = n / N
Inclusion probability without replacement: π = n / N
Inclusion probability with replacement: π = 1 - (1 - 1 / N)^n
Number of samples without replacement: C(N, n) = N! / [n!(N - n)!]
Number of ordered draws with replacement: N^n
Finite population correction: FPC = sqrt((N - n) / (N - 1))
How to Use This Calculator
- Paste your population list in the text box.
- Choose the delimiter used in your list.
- Enter the required sample size.
- Select sampling with or without replacement.
- Add a seed when you need repeatable output.
- Use the numbered population option when you only know N.
- Press the calculate button.
- Review the sample above the form.
- Download the selected units as CSV or PDF.
Simple Random Sampling Guide
What It Means
A simple random sample gives each unit a known chance of selection. It is one of the clearest sampling methods in statistics. The idea is direct. Build a complete population list. Then choose units by chance, not by judgment.
Why This Calculator Helps
This calculator helps you do that process fast. You can paste names, IDs, product codes, customer records, survey rows, or any other units. You can also enter only the population size. The tool then creates numbered units for you. This is useful when you want record numbers instead of labels.
Repeatable Sampling
The seed option supports repeatable work. Use the same population, sample size, method, and seed. The same sample will appear again. This is helpful for audit trails, classroom examples, and documented research. Leave the seed blank when you want a fresh draw each time.
Replacement Options
Sampling without replacement is common for surveys. A unit can appear only once. The inclusion probability is n divided by N. Sampling with replacement lets the same unit appear more than once. This method is useful for simulation, bootstrapping, and probability demonstrations.
Useful Measures
The calculator reports the sampling fraction, possible sample count, and finite population correction. These values help you understand the design. A larger fraction means the sample covers more of the population. A small finite correction can reduce standard error in some estimates.
Data Preparation
Good sampling still needs good preparation. The population list should be current. It should not miss important groups. It should not duplicate records unless duplication is intentional. Clean labels make the output easier to verify.
Best Use Cases
Simple random sampling works best when every unit can be listed. It is less useful when the population is hidden, changing, or difficult to number. In those cases, stratified, cluster, or systematic methods may fit better.
Documentation
For sensitive studies, store the seed and settings with care. They show how the draw was made. This improves transparency. It also helps another analyst repeat the selection without guessing or bias.
Final Step
Use this page before a survey, quality check, classroom exercise, or data audit. Start with a trusted list. Select your method. Add a seed when repeatability matters. Review the selected units. Then export the results for reports, worksheets, or documentation.
FAQs
What is a simple random sample?
It is a sample selected by chance from a full population list. Each unit has a known selection probability. Without replacement, each unit can appear only once.
What does sample size mean?
Sample size is the number of units selected from the population. It is shown as n in formulas. Larger samples usually provide more stable estimates.
What does population size mean?
Population size is the total number of eligible units. It is shown as N. The calculator counts pasted items or uses the numbered population option.
Should I sample with replacement?
Use replacement for simulations, bootstrap examples, or repeated probability draws. Use no replacement when selecting real survey records or unique inspection units.
Why should I use a random seed?
A seed makes the random draw repeatable. The same inputs and seed return the same sample. This helps with audits, teaching, and reports.
What is inclusion probability?
It is the chance that a specific population unit appears in the sample. Without replacement, it equals sample size divided by population size.
What is finite population correction?
It adjusts standard error when sampling without replacement from a limited population. It becomes more important when the sampling fraction is large.
Can I export the sample?
Yes. Use the CSV button for spreadsheet work. Use the PDF button for reports, records, or printable documentation.