Daniel Levitin: Lie guide

The Publishing House of Mann, Ivanov and Ferber, with the support of the Evolution Foundation, has published a book of a cognitive psychologist, professor of McGill University in Montreal Daniel Levitin, “Lie guide . Critical thinking in the era of post -truths. " In it, the author demonstrates techniques that are often used for manipulations with numerical data, and the methods that can be verified by the statements distributed by the media. Based on the fact that people tend to apply critical thinking only to what they disagree with, Levitin demonstrates how people can “deceive and mislead numbers and logic” and offers strategies to recognize cognitive prejudices and logical errors

With the permission of the publishing house, we publish an excerpt from this book, dedicated to various manipulations using "average meaning".

Czech with medium

The average value can be very useful, and it is easier to deal with it than with a circular diagram. It allows us to characterize a huge amount of information with one single number. For example, we want to know the average well-being of people in the room in order to understand whether a meeting with them will bring any benefits to our Fandraizers* or sales managers. Another example: we want to know the average gasoline price in order to evaluate how much a trip to a car from Vancouver to Banf will cost. However, the middle can be deceptively complicated.

There are three types of medium, and they can be expressed by different numbers. Therefore, those who seriously engage in statistics avoid the words “average”, giving preference to other, more accurate terms, such as: the arithmetic mean , median or fashion . And only so. Sometimes all these values ​​coincide, but more often they differ. If you have met the word “average”, it usually means “mean arithmetic”, but you cannot be absolutely confident in this.

More often than others, the arithmetic mean of these three; It is equal to the sum of all data divided by their number. For example, the average well -being of all people in the room will be equal to their general well -being, divided into the number of people. If there are ten people in the room, the state of each of which is estimated at 100 thousand dollars, then the total wealth will be a million. From here it is easy to calculate the arithmetic mean (you don’t even need to get a calculator): 100 thousand dollars. And if the state of each present will vary from 50 thousand to 150 thousand dollars, but the total number will still be a million, then the average arithmetic will still be 100 thousand dollars (because we simply divide a million by ten, without taking into account how much money is in the account).

Median is a number in the middle of an ordered set of numbers (statistics are called a sample): half of the data is below this value, and half higher. As you remember, the meaning of the average value is to characterize the entire amount of data with one single number. Mediana does it better with this if some of your data is very different from the majority, statistics are called such values ​​emissions .

Imagine a room in which nine people are located; The state of the eight of them is about 100 thousand dollars, and one is on the verge of bankruptcy, its debt is 500 thousand dollars. Here's what we will succeed:

Man 1: –500 thousand dollars.
Man 2: 96 thousand dollars.
Man 3: 97 thousand dollars.
Man 4: 99 thousand dollars.
Man 5: 100 thousand dollars.
Man 6: 101 thousand dollars.
Man 7: 101 thousand dollars.
Man 8: 101 thousand dollars.
Man 9: 104 thousand dollars.

Now we add all the indicators and get a total amount of $ 299 thousand. We divide this number into the total number of participants, nine, and it turns out that the arithmetic mean is 33,222 dollars. However, the impression is created that the arithmetic mean is not the best way to characterize the data on those present. I dare to assume that the fundraiser will not want to make a visit to them if there is a person among them with an indicator, who pulls the whole group down. This is the whole difficulty of working with the arithmetic mean: it is too sensitive to emissions.

Median here is equal to 100 thousand dollars: four earn less than this amount, and four more. Fashion is 101 thousand dollars - this is the figure that appears much more often than others. Both median and fashion in this particular example are much more indicative.

You can use the average in different ways, especially if you want someone to see in your data what you need.

Let's imagine that you and two friends launched a startup - a small company in which five people work. Now is the end of the year, you are going to summarize the financial results and tell the employees how the company is doing things so that they feel satisfaction from the long hours spent in the office and from the cold pizza, eaten during this time. And you also want to attract investors. Let's say four employees-all programmers-earned 70 thousand dollars in a year, and one-an office manager-50 thousand. This will give the arithmetic mean salary equal to 66 thousand dollars per year: the amount (4 × 70 000) + (1 × 50,000), divided by 5. You and your two friends brought 100 thousand dollars home - this is your salary. Therefore, the total amount of salaries paid will be (4 × 70 000) + (1 × 50,000) + (3 × 100,000) = 630 thousand dollars. In addition, let your company bring 210 thousand dollars of net income, which you divided equally to each other and co -founders as bonuses, this gives each of you 100 thousand + 70 thousand. How will you tell them about this?

You could say:

The average salary of employees is 66 thousand dollars;
The average salary + profit of the owners is 170 thousand dollars.

And although this is true, it is unlikely that someone will like the news except you and your mother. If your subordinates find out about this, they will decide that they have significantly undercomed. And potential investors will consider that the founders pay too much. Therefore, you can make a report differently:

The average salary of employees is 66 thousand dollars;
The average salary of owners is 100 thousand dollars;
Profit: 210 thousand dollars.

For potential investors, this looks more convincing, especially since they can not say that you have divided the profit between co -owners. And employees can not show the last line at all. Each of the four programmers will think that he is in good account and appreciated him, as he earns more than the majority. The only one who will not be very pleased is your office manager. But the girl had previously understood that programmers earn more of her. Now imagine: you feel that they are overloaded with work, and want to persuade your partners who are not strong in critical thinking, that you need to hire more employees. You can do the same as many companies do in this case, and declare “profit for one employee”, dividing the company's profit equal to 210 thousand dollars, by five:

The average employee salary: 66 thousand dollars;
The average salary of the owners: 100 thousand dollars;
An annual profit per employee: 42 thousand dollars.

Now you can say that 64 % of the salary that you pay to your employees (42,000 / 66,000) return to you in the form of profit, and this means that in the end, having made a profit, you will have to pay only 36 % of their salaries. Of course, these data do not indicate that, by hiring another employees, you will increase profits. But in the eyes of the one who is not very strong in critical thinking, it looks like a significant argument to increase the state.

But what if you want to look like an incredibly honest and fair employer and show that the difference between your profit and the salary of your employees is quite reasonable? Take a profit of 210 thousand dollars and divide part of this amount, 150 thousand dollars, as a bonus between yourself and your partners. You will say about the remaining 60 thousand later that this is “profit”. This time, calculate the average salary by including yourself and your partners in these calculations with bonuses:

Average salary: 97 500;
The average profit of the owners of the company: 20 thousand.

And now we will really have fun:

General salary payments plus bonuses: 840 thousand;
salaries: 780 thousand;
Profit: 60 thousand.

Now everything looks reasonable, right? Of the entire amount of 840 thousand dollars, including salary and profit, only 60 thousand, or 7 %, amounted to personal profit of the owners. Your employees will think that you are impeccable - who will blame the owner of the company of assigning 7%? In fact, this is not so much: 7% is divided between the owners of the company equally, and everyone gets 2.3%. Yes, there is nothing to object!

And you can come up with something better. Imagine that in the first year of your company you had only employees who worked for a part day. They earned 40 thousand a year. In the second year you had only employees who worked full day. And they received 66 thousand, which were mentioned above. In this case, you can say with all confidence that on average, the earnings of each employee increased by 65%. You are a great entrepreneur! True, you are silent that you compare two incomparable things: work on incomplete and complete working days. I can say that this is not the first in this: the American corporation for production became US Steel thought before that in the 1940s.

* Fundraiser (Fundraiser, English) - the one who provides services to attract resources independently or under a contract. Approx. Ed.