What is normal distribution? What is the 28 law?

If you are a programmer , Should have been used in programming Random （random） function . Its function is to randomly generate some numbers within a specific value range . This function is preset in many programming languages , Can be called directly .

for example , From you to 1 To 100 Randomly generate an integer between , When writing a program, it is necessary to define a 1 To 100 Value range of , Then call the random function , A random number with equal probability in the range is obtained , That is to say 100 The probability of any number appearing in the number is 1/100.

Programmers who are used to random functions will mistakenly think that “ Random ” It represents uniformly distributed data , Equal probability event . This is a mistake . in real life , Most randomness is not uniformly distributed .

for instance , We know that the probability of flipping a coin upside down is half , But if you do throw 10 The second coin , You will find that the coin just has 5 The probability of a sub head up is neither 50%, Neither 10%, But in 25% about . Because in nature , The most common “ Random ” It's a normal distribution （ Also known as Gaussian distribution ）, The distribution curve is “ Bell shape ”

The normal distribution is the probability distribution of a group of data in the normal state . Only two parameters are needed to describe this distribution ： The first is the data Average , Usually in Greek letters μ To express , It is located in the middle of the function image . Two is Standard deviation , Usually in Greek letters σ To express , It represents the degree of dispersion of this set of data . The smaller the standard deviation , The more centralized the data is , On the contrary, the more scattered the data is .

Suppose a set of data obeys a normal distribution , According to the distribution characteristics , Among them is 68% The number of will focus on the average plus or minus 1 Within the range of standard deviation , Yes 95% The number of will focus on the average plus or minus 2 Within the range of standard deviation , Yes 99.7% The number of will focus on the average plus or minus 3 Within the range of standard deviation . because 3 The range of standard deviation covers almost all the data , So it is widely used in mathematics , It is suitable for derivation and estimation in many scenarios .

In a nutshell , The normal distribution shows “ A lot in general , Extremely few ” The phenomenon of . This phenomenon is very common in life . such as , Most people are within a range of height , Not many people are too tall or too short . Observe the people around you carefully , It can be found that very smart or very stupid people are very few . Statistics on the income of the whole society , There are more people with medium income , There are fewer people who are particularly poor and wealthy .

It's often said This rule （ Also known as Pareto Law ）, Just another way to describe the normal distribution phenomenon . The two eight rule tells us ,20% Of the rich in the world 80% The wealth of ; Just master the dictionary 20% You can understand the article with your own words 80% The content of ;20% Living in the megacity of 80% Population , wait .

The properties of normal distribution have other wide applications . We know , Using multiple sampling, a convincing overall conclusion can be drawn from a relatively small number of data . For example, just research 100 personal , We can roughly understand the general psychological cognition of human beings . Just spot check 100 Commodity , We can draw a conclusion about the quality of this batch of goods .

These polls 、 Commodity sampling , Are using sampling samples to estimate the population , The mathematical principle behind it is Central limit theorem . The central limit theorem proves theoretically , No matter what the distribution of random variables is , As long as the number of samples is large enough , The average value of the sample will approximately follow the normal distribution .

in other words , Although everyone or every product will be affected by a large number of random factors , These factors will have some influence on the final state , But we don't have to worry about the details of these factors , As long as people or goods are regarded as a whole . The statistical law of the whole obeys the normal distribution .

And these things , In the real world “ Random ”.