Symmetrical distributions {normal distribution} {normal curve} {Gaussian curve} {Gaussian distribution} over continuous domain can have highest frequencies near mean and lowest frequencies farthest from mean. y = (1 / (s * (2 * pi)^0.5)) * (e^(-(x - u)^2 / (2 * s^2))), where x is domain value, y is frequency, u is mean, and s is standard deviation.
median
In normal distributions, mean equals mode equals median.
approximations
Non-normal distributions can transform to normal distributions using square root of x or logarithm of x.
purposes
Normal distribution models random errors {error curve}. Normal distributions result from measurements that have many factors or random errors. For example, height results from genetics, diet, exercise, and so on, and has normal distribution.
Passing inputs through different-threshold sigmoidal functions, and then finding differences, results in Gaussian distributions.
theorem
If many random same-size samples come from a large population with normal distribution, sums of samples make a normal distribution {central limit theorem, normal distribution}, as do sample means.
mean
Sample-mean mean is an unbiased population-mean estimate.
Mathematical Sciences>Statistics>Distribution
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Date Modified: 2022.0224