Calculator Inputs
Large screens use 3 columns, smaller screens use 2, mobile uses 1.Example Data Table
| Scenario | Min | Max | Count | Type | Distribution | Seed | Sample Output |
|---|---|---|---|---|---|---|---|
| Dice Simulation | 1 | 6 | 12 | Integer | Uniform | 42 | 6, 3, 5, 1, 2, 4... |
| Classroom Sampling | 10 | 50 | 8 | Integer | Uniform | 101 | 13, 27, 42, 19, 31... |
| Measurement Noise | 0 | 1 | 10 | Decimal | Normal | 77 | 0.48, 0.61, 0.43, 0.55... |
| Lottery Picks | 1 | 49 | 6 | Integer | Uniform | 555 | 5, 11, 23, 31, 38, 44 |
| Score Modeling | 0 | 100 | 20 | Decimal | Normal | 900 | 64.21, 57.84, 71.10... |
Formula Used
1) Seeded generator core:
Xn+1 = (aXn + c) mod m
2) Uniform integer formula:
value = min + floor(u × (max - min + 1))
3) Uniform decimal formula:
value = min + u × (max - min)
4) Normal distribution formula:
z = √(-2 ln(u₁)) × cos(2πu₂)
value = mean + stddev × z
5) Summary statistics:
Mean = sum / count, Range = max - min, Variance = average squared distance from mean, Standard deviation = √variance.
How to Use This Calculator
- Enter the minimum and maximum allowed values.
- Choose how many random numbers you want.
- Select integer or decimal output.
- Pick uniform or normal distribution.
- Set decimal places, repeat rules, sorting, and an optional seed.
- For normal distribution, enter mean and standard deviation.
- Click Generate Numbers to show results above the form.
- Review the chart, table, and summary statistics.
- Use the CSV or PDF buttons to export your results.
Frequently Asked Questions
1. What does the seed value do?
A seed makes the generator repeat the same sequence later. Use the same settings and seed to recreate identical results for lessons, testing, or documentation.
2. When should I use uniform distribution?
Use uniform distribution when every value in the allowed range should have an equal chance. It suits dice simulations, random picks, classroom tasks, and general testing.
3. When should I use normal distribution?
Use normal distribution when values should cluster around a central mean. It is useful for score modeling, measurement noise, sampling exercises, and many natural processes.
4. Can I generate unique values only once?
Yes. Set repeats to “No” for uniform integers. The calculator then avoids duplicates. This option is not used for decimals or normal outputs because uniqueness becomes less meaningful there.
5. Why are decimal results rounded?
Decimal places help keep output readable and consistent. Rounding also makes exported tables cleaner, especially when you need classroom examples, reports, or quick comparisons.
6. What do the summary statistics show?
They describe the generated dataset. You can inspect count, minimum, maximum, mean, median, range, and standard deviation to understand spread and central tendency quickly.
7. Can I export the generated numbers?
Yes. Use the CSV button for spreadsheet-ready output and the PDF button for a shareable report. Both exports include the generated numbers and key settings.
8. What happens if minimum equals maximum?
The generator returns the same boundary value each time. This is valid mathematically, though the output has no spread because the allowed range contains only one value.