2sigma principle: the probability of numerical distribution in (μ-2σ, μ+2σ) is 0.9544;

3sigma principle: the probability of numerical distribution in (μ-3σ, μ+3σ) is 0.9974;

In normal distribution, σ represents standard deviation, μ represents mean value, and x=μ is the symmetry axis of the image.

3σ criterion, also known as Leda criterion, assumes that a set of test data only contains random errors, calculates and processes them to get the standard deviation, and determines an interval according to a certain probability. It is considered that any error beyond this range is not random error, but gross error, and the data containing this error should be excluded. 3σ is suitable for the case of multiple sets of data.

It can be considered that the numerical distribution is almost all concentrated in the range of (μ-3σ, μ+3σ), and the possibility of exceeding this range is less than 0.3%.

Extended data:

Normal distribution, also known as "normal distribution" and Gaussian distribution, was first obtained by A. de moivre in the asymptotic formula of binomial distribution. C.F. Gauss deduced it from another angle when studying the measurement error. Laplace and Gauss studied its properties.

It is a very important probability distribution in mathematics, physics, engineering and other fields, and has great influence in many aspects of statistics. The normal curve is bell-shaped, with low ends and high middle, which is symmetrical left and right, so people often call it bell-shaped curve.

If the random variable X obeys the normal distribution with a mathematical expectation of μ and a variance of σ 2, it is recorded as N(μ, σ 2). The expected value μ of probability density function with normal distribution determines its position, and its standard deviation σ determines its distribution amplitude. When μ = 0 and σ = 1, the normal distribution is standard normal distribution.

Baidu Encyclopedia-Normal Distribution