1, concentration: the peak of the normal curve is located in the center, that is, where the average value is located.

2. Symmetry: The normal curve is centered on the mean value, which is symmetrical left and right, and both ends of the curve never intersect with the horizontal axis.

3. Uniform variation: the normal curve starts from the place where the mean value is located and gradually decreases evenly to the left and right sides respectively.

Second, the limit error refers to the maximum range of error guaranteed by a certain probability in sampling inference, so it is also called allowable error. The upper limit of confidence interval is formed by estimator plus allowable error, and the lower limit of confidence interval is formed by estimator minus allowable error. The limit error is expressed as the critical value (or probability degree) of a certain confidence multiplied by the sampling average error. Namely: limit error = critical value x sampling average error.

Three, the error value usually take two, can also take only one.

Error calculation formula

Nominal error = (maximum absolute error)/range x 100%

Absolute error = | Indication-standard value | (that is, the absolute value of the difference between the measured value and the real value).

Relative error = | Indication-standard value |/true value (i.e. absolute error as a percentage of true value).

System error: it is the error caused by measuring tools and fixtures.

Accidental error: it is an accidental error caused by the operator's operation (or external factors).

Four, in the general calculation, the best estimate of the true value generally takes the arithmetic average.

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.

References:

Baidu Encyclopedia: Gaussian Distribution? Baidu Encyclopedia: Limit Error