Gaussian (Normal) Random Number Generator
Draw values from a bell-curve distribution instead of a flat uniform range — set your own mean and standard deviation for realistic simulated data.
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How the Gaussian (Normal) Random Number Generator works
Most random number generators — including Xrandom's own number generator above — produce a uniform distribution, where every value in a range is equally likely. Real-world quantities like human heights, test scores, and measurement error rarely behave that way; they cluster around an average and taper off symmetrically, forming the familiar bell curve known as the Gaussian or normal distribution.
This tool converts uniform random draws into normally distributed ones using the Box–Muller transform, a classic technique that takes two independent uniform random numbers and produces a pair of independent standard normal values, which are then scaled by your chosen standard deviation and shifted by your mean.
How to use it
Frequently asked questions
What's a realistic standard deviation to use?
It depends entirely on your data. For IQ scores, a mean of 100 and standard deviation of 15 is standard; for your own data, use the observed or expected standard deviation of the quantity you're modelling.
Can values fall far from the mean?
Yes, in principle any value is possible, though about 99.7% of draws fall within three standard deviations of the mean, matching real Gaussian behaviour.
Why use this instead of a flat random number?
Use this whenever you're simulating a naturally occurring quantity that clusters around an average rather than one where every outcome is equally likely, such as dice rolls or lottery numbers.