Random Number Generator

Type of Random Numbers

Integers

Whole numbers

Uniform

Decimal numbers

Normal

Bell curve

Random Sample

From list

Minimum Value

Maximum Value

How Many Numbers

Generate

Quick Generators

🎲 Roll a Die1-100🪙 Flip a CoinIQ Scores (μ=100, σ=15)

About Random Number Generation

• • Integers: Uniformly distributed whole numbers between min and max (inclusive)
• • Uniform: Decimal numbers with equal probability across the range
• • Normal: Bell-curve distribution using the Box-Muller transform
• • Random Sample: Select items from a list with or without replacement

How to Use the Random Number Generator

This tool generates random numbers for various statistical and practical applications. Choose from four generation modes.

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Generation Types

Random Integers

Generate whole numbers within a specified range. Each number in the range has an equal probability of being selected.

Use cases:

• Rolling dice
• Lottery numbers
• Random selection
• Simulations

Uniform Distribution

Generate decimal numbers uniformly distributed across a range. Every value in the interval has equal probability density.

Use cases:

• Monte Carlo simulations
• Random sampling
• Generating random percentages

Normal (Gaussian) Distribution

Generate numbers following a bell curve distribution, clustered around a mean with specified standard deviation.

Parameters:

• Mean (μ): Center of the distribution
• Standard Deviation (σ): Spread of values

Use cases:

• Simulating test scores
• Modeling natural phenomena
• Statistical sampling
• Error simulation

Random Sample

Select items randomly from a custom list. Choose sampling with or without replacement.

Use cases:

• Drawing names from a hat
• Random assignment to groups
• Survey sampling
• Randomized order

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Statistical Properties

Uniform Distribution

Property	Value
Mean	(min + max) / 2
Variance	(max - min)² / 12
Std Dev	(max - min) / √12

Normal Distribution

Property	Value
Mean	μ (user specified)
Variance	σ²
68% of values	Within μ ± σ
95% of values	Within μ ± 2σ
99.7% of values	Within μ ± 3σ

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Common Applications

Dice Rolling

• Single die: min=1, max=6
• Two dice sum: Generate 2 numbers, add them
• D20 (role-playing): min=1, max=20

Coin Flipping

• min=0, max=1
• 0 = Tails, 1 = Heads

Card Drawing

Enter 52 cards as a list, sample without replacement

IQ Score Simulation

• Normal distribution
• Mean = 100
• Standard Deviation = 15

Exam Scores

• Normal distribution
• Mean = 75 (typical class average)
• Standard Deviation = 10-15

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About Random Number Generation

True vs. Pseudo-Random Numbers

This tool uses pseudo-random number generation (PRNG), which uses mathematical algorithms to produce sequences that appear random. For most statistical applications, this is sufficient.

For cryptographic applications, use a cryptographically secure RNG instead.

Quality of Randomness

The JavaScript Math.random() function used here provides:

• Uniform distribution
• Period long enough for typical applications
• Sufficient for simulations and sampling

Reproducibility

Each generation produces different results. For reproducible simulations, consider using a seeded random number generator (not available in this tool).

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Sampling Methods

With Replacement

• Items can be selected multiple times
• Each draw is independent
• Sample size can exceed population size
• Probability stays constant

Without Replacement

• Each item can only be selected once
• Draws are dependent
• Sample size ≤ population size
• Probability changes after each draw

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Best Practices

For Statistical Sampling

1. Define your population clearly
2. Use simple random sampling when possible
3. Generate more samples than needed to account for exclusions
4. Document your sampling method

For Simulations

1. Generate sufficient replications (often 1,000+)
2. Check that results match expected distributions
3. Use appropriate distribution for your model
4. Consider edge cases

For Random Assignment

1. Use without replacement for unique assignments
2. Balance group sizes if needed
3. Document the randomization for reproducibility

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Related Resources

• Probability Basics - Understanding randomness
• Normal Distribution - The bell curve
• Sampling Methods - Types of sampling
• Monte Carlo Methods - Simulation techniques