# Ferimi Estimation

Fermi estimation is a method for obtaining rough numbers (data).

Well-known examples are "How many Japanese cats?" And "How many telephone poles in Japan?"

Even if you don't know the answer number at all, Fermi estimation is a rough calculation of the answer number.

## Example of Fermi estimation

For example, suppose you want to estimate "How many elementary school students are in City A?"

The formula is
"number of schools" * "number of people per school".

Number of schools = 20
number of people per school = 500

Then,
20 * 500 = 10000
will be obtained.

In Fermi estimation, it is important to know that "the number of digits is about 4 0s", and it will be used for subsequent decision making. The fact that the largest digit is "1" is not very important. Rather, it's a rough number, so it's easy to fail if the measure is exactly the same as "1".

Depending on the number you put, it may be doubled or halved, but I don't really care about that. In Fermi estimation, it is considered that the result is that it is not a number as large as 1000 or 100000 at least.

## Two points of Fermi estimation "Utilization of data in the head" and "Creation of calculation formula"

There are two important points in the Fermi estimation. "Utilization of the data in my head" and "Creation of calculation formula". Creating formulas is also known as "factorization."

First, consider the calculation formula. Next, apply the data in your head to the formula. By doing this, we will derive numbers that cannot be understood by themselves.

In addition, if there is an accurate value or calculation formula, it is better to use it because it may be a part.

The data in your head can be useful even in situations where you don't have a formula. This is useful in situations where there is no data.

For example, when improving work hours, we may receive the opinion that "the work hours are not recorded anywhere, so we do not know the current time."

However, when I ask the person who is always doing the work at such times, "How many minutes does this work usually take as a guide?", It feels like "30 minutes", and the desired data is obtained. I have taken it. In this case, the data of each working time was obtained with the roughness of about 10 minutes. At this time, the data was sufficiently accurate for the first survey.

A similar question is, "How often does this trouble occur? Is it daily? Is it once a month? Is it once a year?" You may get an answer as to which one is closer. This alone will help you decide what to do next.

### Mathematical modeling is used to create formulas.

Fermi estimation is a type of Mathematical Modeling . Create a formula using hypotheses and principles.

A method of creating a formula by Quality Way of Making Hypothesis, identifying items (factors) that are likely to be included in the formula, and then asking "Which of the items is the relationship of addition, subtraction, multiplication, or division?" There is also.

Dimension Analysis allows you to check the correctness of the formula you created from the aspect of the unit.

## Application of Fermi estimation

### Fermi estimation for immeasurable things

" Risk " and " productivity " can be imagined, but cannot be measured directly.

However, if you formulate these well, you may know and be able to measure the approximate numbers for each factor.

• Risk = Frequency of occurrence * The magnitude of damage when it occurs
• Productivity = Volume produced / Time taken for production

### Prediction and simulation

Fermi estimation can be used for prediction and simulation.

For example, with regard to the above risks, it becomes possible to understand that "if the frequency of occurrence can be halved, the risk can be halved."

## Largest digit is important for accuracy

If you know the Significant Figures , it is easy to understand the points that you should stick to.

For example, in the above example, the number of students per school is set to "500", but even if you say "the exact value is 503" and include 503, the final number does not change much. On the other hand, if you say "the exact value is 100" and enter 100, it will change considerably.

For Fermi estimation, the accuracy of the largest digit of each data is important.

When improving the formula, the point of improvement is the factor that affects the number of digits of the final estimate.

If the number of digits of the largest digit changes, the number of digits of the estimated value may change, so in that sense as well, it is important to look at the number of digits of the largest digit.