Interesting explanation of "normal distribution"

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Suppose your mother is very worried about your single life and is afraid that you will die alone. In order to find high-quality blind dates for you, we put your photos on the blind date website.

Emma, ??this suddenly attracted more than 200 people to leave messages, asking for a "private life-long contract" with you.

My mother can be said to be the Queen Mother who descended to earth. In order to improve the screening efficiency, she created a WeChat group to let everyone report their accurate height.

Fortunately, my mother did some simple statistics work back then. She counted the number of people in each section of 5 centimeters in units of 5 centimeters. Then, using height as the horizontal axis and number of people as the vertical axis, the following picture was drawn.

Looking carefully at this picture, you and your mother discovered a surprising secret: the shape of this picture is high in the middle and low on both sides, and it looks like an upside-down clock.

In fact, human height conforms to the normal distribution.

In 2017, the average height of adult males aged 18 and above in my country was 167.1cm.

Then based on the normal distribution of height, we can quickly know that the height of most men is concentrated at the average value, and the height of a small number of people is either slightly higher or slightly lower than the average height.

The amazing thing is that whether it is people's height, arm length, lung capacity, or their test scores, they all conform to the normal distribution.

This starts with the person who invented this stuff.

Victorian scholar Francis Galton was fascinated by data distribution and built a device that could produce "data distribution". He found that this shape worked well for a lot of data, and he named it "The Normal Distribution."

The English word normal is "normal", which means "common, typical", mainly because this distribution can appropriately represent a variety of data types.

1) Employee performance

The performance of most employees is average. There are very few who do particularly well, and very few who do particularly poorly. This is why in the field of performance management, the "vitality curve" is used to evaluate performance.

What is the "vitality curve"?

It is obviously not good to have a high employee turnover rate. According to calculations, the recruitment process costs about 50% of the employee's annual salary. Excessive employee turnover means out-of-control recruitment costs. The performance loss due to resignation is about 30-400 of the employee's annual salary. Excessive employee turnover rate means huge performance losses.

Too low employee turnover is not good either. Very low employee turnover often comes from a tolerance for poor performance. Allowing poor performers to stay on the team will not only result in a loss of wages, but also the performance that should have been achieved. Additionally, a poor performer is often more reluctant to leave because he may not be able to find another job. For the sake of safety, he will find ways to squeeze out people with good performance, and your team will become less and less effective.

Jack Welch, the former CEO of General Electric, believes that it is easy for everyone to realize the problem of too high employee turnover rate, but it is difficult to realize the harm of too low turnover rate. Therefore, he put forward the famous "Last place elimination system" (also called "vitality curve"), he divided employees into:

This system is considered to be one of the magic weapons that brings unlimited vitality to General Electric.

Therefore, don’t be lazy at work in the future, or you will be laid off by your boss. Scared?

2) Product quality

The quality of most products is mediocre. There are very few truly good products, but there are also very few products that are rotten to the core. This is why in the field of quality management, 6 standard deviations are used to eliminate unqualified products.

3) Find a parking space quickly

According to the Wall Street Journal, Americans even park in shopping malls with a normal distribution, facing the mall entrance. The largest number of parking spaces is the "peak" of the normal curve, and the number of parking spaces gradually decreases on the left and right sides of the entrance, which is the "tail" where both ends of the curve decline.

After you know this rule, the next time you park your car, you can directly choose a place with fewer cars at both ends of the last entrance. The probability of finding a parking space will be much higher.

4) IQ

The IQ of most people is normal, and only a few people like Mr. Einstein have crazy IQs.

5) Predict the location of the data

A magical thing about the normal distribution: the location of the data can be roughly estimated.

Let’s start with an example.

If you choose the right personal business model and successfully open a company, hundreds of employees will take the subway to work in the company in the morning.

Your company can be thought of as the middle position in the diagram below. Some people can get to the company by taking 3 subway stops, some can get to the company by taking 2 stops, and many people live relatively close and can get to the company by taking 1 subway stop. The stops here indicate how far away you are from the company.

The above graph is actually the normal distribution graph below

The line in the middle represents the mean (the position of the company in the example).

Standard deviation represents the fluctuation of data.

1 standard deviation represents a location that is 1 standard deviation away from the mean (in the example, it is 1 station away from the company). Similarly,

2 standard deviations and 3 represent distances. The position of 2 standard deviations from the mean,

3 standards means the position of 3 standard deviations from the mean.

What is the use of knowing the distance of these three standard deviations from the mean?

This is of great use.

The "beauty" of the normal distribution, like Michael Jordan's strength, dexterity and elegance on the court, comes from the fact that we can clearly know through the above picture:

There are 68.2 values ??that are within 1 standard deviation of the mean

There are 95.4 values ??that are within 2 standard deviations of the mean

There are 99.7 values Within 3 standard deviations

This may sound silly, but in fact it is one of the fundamentals of statistics.

This is also the most powerful " trump card " of the normal distribution. It is precisely this feature that gives rise to the central limit theorem, a weapon in statistical probability.

A typical example is that every SAT exam (known as the American College Entrance Examination) is carefully designed to obtain a normal distribution of scores with a mean score of 500 and a standard deviation of 100.

This will ensure fairness, so that most people can pass the exam, while a small number of people fail.

Let’s go back to the question we asked at the beginning:

The normal distribution is the most common distribution in the business world.

When there are many factors that affect the result (or success) and no single factor can completely affect the result, the result usually presents a normal distribution.

Many things can be represented by a normal distribution curve, or to assist thinking. For example, the acceptance of technological innovation basically conforms to the normal distribution...

Individuals in the crowd If divided by ability, the distribution should roughly conform to the normal distribution curve:

There is a "gap" in it, which is intended to show that many people will encounter insurmountable obstacles when their abilities increase to a certain level. chasm.

The business model in which you go to work in a company is also consistent with the normal distribution.

That is to say, most people are in the middle average position. They are neither rich nor poor enough to end up on the streets. And becoming a corporate executive is something only a few people can do. Because your "marginal cost" is not zero.

What is "marginal cost"?

Marginal cost refers to the additional cost incurred by a company for each additional product it produces.

You can simply understand that marginal cost is:

When you do something, you need to pay more for each additional output.

So going to work in the company is not an income with zero marginal cost. For every extra dollar of salary income you earn, you have to put in more corresponding work. Not only is the marginal cost of wage income not zero, but in many cases, its marginal cost is increasing.

The increase in marginal cost means that you have to work overtime day and night, and you have to sacrifice a lot of time with family and friends, so that you can achieve an increase in salary income, such as getting a year-end bonus.

We often say that enterprises need to transform, traditional enterprises need to upgrade, and the number of high-tech enterprises needs to be increased. The fundamental of upgrading and transformation is actually to change the cost structure from increasing to more efficient decreasing, even close to zero.

The higher the "marginal cost" of an industry, the more fragmented the market is, conforming to the normal distribution: fewer people make big money, fewer lose big money, and most people tend to earn average profits.

Back to the question raised at the beginning: Why can’t you become a company executive even though you work very hard?

The answer is very simple, because the personal business model you choose to work and receive wages is a normal distribution, and most people cannot become executives.

Therefore, the personal business model you choose to work and receive wages is a normal distribution, and most people cannot become executives.

Note that what I say here is "mostly", which means I am looking at the problem from an overall perspective.

If you say that someone around you is a senior executive, sorry, you are looking at the problem from a special sample.