Calculator
Example Data Table
| Case | Population value | Selected in sample | Note |
|---|---|---|---|
| 1 | 12 | Yes | Lower value |
| 2 | 15 | Yes | Repeated value |
| 3 | 17 | No | Middle value |
| 4 | 19 | Yes | Above mean |
| 5 | 22 | No | Upper value |
Formula Used
Mean: x̄ = Σx / n
Sample variance: s2 = Σ(x - x̄)2 / (n - 1)
Standard error: SE = s / √n
Finite population correction: FPC = √((N - n) / (N - 1))
Confidence interval: x̄ ± critical value × SE
Needed sample size: n = (z × s / E)2
How to Use This Calculator
- Enter numbers separated by commas, spaces, or line breaks.
- Choose whether values are already a sample or a population list.
- Select a random sampling method and sample size.
- Enter the confidence level, population size, and optional known SD.
- Press calculate to show results above the form.
- Use CSV or PDF buttons to save the report.
Random Samples in Statistical Work
Why random sampling matters
A random sample gives each eligible item a known chance of selection. This simple rule protects the study from hidden preference. It also helps one small group represent a much larger population. Good sampling does not guarantee perfect answers. It reduces bias and gives uncertainty a measurable shape.
What this calculator estimates
This calculator turns selected values into useful summaries. It reports count, mean, median, variance, standard deviation, and standard error. It also builds a confidence interval for the population mean. When a population size is supplied, the finite population correction can reduce the standard error. This matters when the sample is a large share of the population.
Choosing a sampling method
Simple random sampling works well when every record can be listed. Sampling without replacement is common for surveys, audits, and classroom examples. Sampling with replacement suits simulation work and bootstrapping ideas. Systematic sampling selects a starting point, then follows a fixed interval. It is quick, but the list should not contain repeating patterns.
Reading the results
The mean is the sample center. The standard deviation shows typical distance from that center. The standard error estimates how much the mean may change across many random samples. A wider interval means less precision. A smaller margin of error means the estimate is tighter. Larger samples usually improve precision, but poor sampling can still damage the conclusion.
Using results responsibly
Random samples support decisions, but context still matters. Check for missing values, impossible entries, and duplicate records. Confirm that the population list matches the question. Record the seed when repeating a generated sample. Explain the confidence level and method in reports. The exported table can support reviews, lessons, and research notes. Use the calculator as a transparent guide, not as a substitute for a sound sampling plan.
Common input checks
Before using any result, review the data source. Remove labels, units, and blank cells from the values box. Keep only numbers separated by commas, spaces, or line breaks. If the sample is generated from a population list, compare the drawn values with the original records. This quick check catches typing errors before they affect the final interpretation. It also improves reproducibility overall.
FAQs
What is a random sample?
A random sample is a selected group where each eligible item has a known chance of selection. It helps reduce bias and supports fair statistical estimates.
Can I paste values from a spreadsheet?
Yes. Paste numbers separated by commas, spaces, or line breaks. Remove labels, symbols, and units before running the calculator.
What does the seed field do?
The seed repeats the same random draw. Use it when you want the same sample again for checking, teaching, or reporting.
When should I use replacement?
Use replacement for simulations, resampling, or bootstrapping ideas. Use no replacement for most surveys, audits, and finite lists.
Why is my interval wide?
A wide interval usually means high variation, small sample size, or a high confidence level. Better data or a larger sample can narrow it.
What is finite population correction?
It reduces standard error when your sample is a large part of a finite population. Enter population size and check the option.
Is the p-value exact?
The p-value is an approximate two-tailed value. It uses a normal approximation, so specialist software may differ for very small samples.
Can I export the result?
Yes. Use the CSV button for spreadsheet use. Use the PDF button after calculation for a printable summary.