The characteristics of random errors subject to normal distribution are: symmetric random errors can be positive or negative, but positive and negative errors with equal absolute values have equal opportunities. That is, f (δ >; The-δ curve is symmetrical with respect to the longitudinal axis. Boundedness under certain measurement conditions, the absolute value of random error will not exceed a certain range, that is, there will be almost no random error with large absolute value. Under the same conditions, when the number of measurements is n→∞, the algebraic sum of all random errors is equal to zero, that is. Random errors with a small absolute value of a single peak are more likely to occur than those with a large absolute value, that is, the probability density of the former is greater than that of the latter, and the probability density of the random error reaches a maximum when δ=0.

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The concept of normal distribution was first put forward by German mathematician and astronomer De Moivre in 1733. But because the German mathematician Gauss first applied it to astronomical research, it is also called Gaussian distribution. Gauss's work had a great influence on later generations, and he also named it "Gauss Distribution". It is precisely because of this work that later generations attributed the invention right of the least square method to him. However, today, the Gaussian head of 10 mark on German banknotes is also printed with a normal distribution density curve.