We have a sequence of numbers, consisting of almost independent elements that obey a given distribution. Usually evenly distributed.

You can generate random numbers in Excel in different ways and ways. Let's take a look at the best of them.

Random Number Function in Excel

1. The RAND function returns a random uniformly distributed real number. It will be less than 1, greater than or equal to 0.
2. The RANDBETWEEN function returns a random integer.

Let's look at their use with examples.

Selecting random numbers with RAND

This function does not require any arguments (RAND()).

To generate a random real number between 1 and 5, for example, use the following formula: =RAND()*(5-1)+1.

The returned random number is evenly distributed over the interval .

Each time the worksheet is calculated, or the value in any cell in the worksheet changes, a new random number is returned. If you want to save the generated population, you can replace the formula with its value.

1. We click on a cell with a random number.
2. Highlight the formula in the formula bar.
3. Press F9. AND ENTER.

Let's check the uniformity of the distribution of random numbers from the first sample using the distribution histogram.

The range of vertical values ​​is frequency. Horizontal - "pockets".

RANDBETWEEN function

The syntax of the RANDBETWEEN function is (lower bound; upper bound). The first argument must be less than the second. Otherwise, the function will throw an error. The bounds are assumed to be integers. The formula discards the fractional part.

An example of using the function:

Random numbers with 0.1 and 0.01 precision:

How to make a random number generator in Excel

Let's make a random number generator with the generation of a value from a certain range. We use a formula like: =INDEX(A1:A10;INTEGER(RAND()*10)+1).

Let's make a random number generator in the range from 0 to 100 with a step of 10.

From the list of text values, you need to select 2 random ones. Using the RAND function, we compare text values ​​in the range A1:A7 with random numbers.

Let's use the INDEX function to select two random text values ​​from the original list.

To select one random value from the list, apply the following formula: =INDEX(A1:A7,RANDBETWEEN(1,COUNT(A1:A7))).

Normal Distribution Random Number Generator

The functions RAND and RANDBETWEEN produce random numbers with a single distribution. Any value with the same probability can fall into the lower limit of the requested range and into the upper one. It turns out a huge spread from the target value.

Normal distribution means that most of the generated numbers are close to the target. Let's correct the RANDBETWEEN formula and create a data array with a normal distribution.

The cost of goods X is 100 rubles. The entire batch produced is subject to a normal distribution. The random variable also follows a normal probability distribution.

Under such conditions, the average value of the range is 100 rubles. Let's generate an array and build a graph with a normal distribution with a standard deviation of 1.5 rubles.

We use the function: =NORMINV(RAND();100;1.5).

Excel calculated which values ​​are in the range of probabilities. Since the probability of producing a product with a cost of 100 rubles is maximum, the formula shows values ​​​​close to 100 more often than the rest.

Let's move on to plotting. First you need to create a table with categories. To do this, we divide the array into periods:

Based on the data obtained, we can form a diagram with a normal distribution. The value axis is the number of variables in the interval, the category axis is the periods.

Etc., and is used by account owners to attract new audiences to the community.

The result of such draws often depends on the luck of the user, since the recipient of the prize is determined randomly.

For such a determination, draw organizers almost always use an online random number generator or a pre-installed one that is distributed free of charge.

Choice

Quite often, it can be difficult to choose such a generator, since their functionality is quite different - for some it is significantly limited, for others it is quite wide.

A fairly large number of such services are being implemented, but the difficulty is that they differ in scope.

Many, for example, are tied with their functionality to a specific social network (for example, many generator applications only work with links of this one).

The simplest generators simply generate a random number within a given range.

This is convenient because it does not associate the result with a specific post, which means that they can be used for draws outside the social network and in various other situations.

They don't really have any other use.

Advice! When choosing the most suitable generator, it is important to consider the purpose for which it will be used.

Specifications

For the fastest process of choosing the optimal online random number generation service, the table below shows the main technical characteristics and functionality of such applications.

All applications discussed in the table are described in more detail below.

randstuff

You can use this application online using the link to its official website http://randstuff.ru/number/.

This is a simple random number generator, characterized by fast and stable operation.

It is successfully implemented both in the format of a separate independent application on the official website, and as an application in .

The peculiarity of this service is that it can choose a random number both from the specified range and from a specific list of numbers that can be specified on the site.

• Stable and fast work;
• Lack of direct link to the social network;
• You can select one or more numbers;
• You can only choose from the given numbers.

User reviews about this application are as follows: “We determine the winners in VKontakte groups through this service. Thank you”, “You are the best”, “I use only this service”.

Cast Lots

This application is a simple function generator, implemented on the official website, in the form of a VKontakte application.

There is also a generator widget to embed on your site.

The main difference from the previous described application is that this allows you to disable the repetition of the result.

Various lotteries, drawings, etc. are often held in many groups or publics on social networks, Instagram, etc., and are used by account owners to attract a new audience to the community.

The result of such draws often depends on the luck of the user, since the recipient of the prize is determined randomly.

For such a determination, draw organizers almost always use an online random number generator or a pre-installed one that is distributed free of charge.

Choice

Quite often, it can be difficult to choose such a generator, since their functionality is quite different - for some it is significantly limited, for others it is quite wide.

A fairly large number of such services are being implemented, but the difficulty is that they differ in scope.

Many, for example, are tied with their functionality to a particular social network (for example, many generator applications on VKontakte work only with links of this social network).

The simplest generators simply generate a random number within a given range.

This is convenient because it does not associate the result with a specific post, which means that they can be used for draws outside the social network and in various other situations.

They don't really have any other use.

<Рис. 1 Генератор>

Advice! When choosing the most suitable generator, it is important to consider the purpose for which it will be used.

Specifications

For the fastest process of choosing the optimal online random number generation service, the table below shows the main technical characteristics and functionality of such applications.

All applications discussed in the table are described in more detail below.

<Рис. 2 Случайные числа>

randstuff

<Рис. 3 RandStuff>

You can use this application online using the link to its official website http://randstuff.ru/number/.

This is a simple random number generator, characterized by fast and stable operation.

It is successfully implemented both in the format of a separate independent application on the official website, and as an application in the VKontakte social network.

The peculiarity of this service is that it can choose a random number both from the specified range and from a specific list of numbers that can be specified on the site.

Pros:

• Stable and fast work;
• Lack of direct link to the social network;
• You can select one or more numbers;
• You can only choose from the given numbers.

Minuses:

• The impossibility of holding a draw on VKontakte (this requires a separate application);
• Applications for VKontakte do not run in all browsers;
• The result sometimes seems predictable, since only one calculation algorithm is used.

User reviews about this application are as follows: “We determine the winners in VKontakte groups through this service. Thank you”, “You are the best”, “I use only this service”.

Cast Lots

<Рис. 4 Cast Lots>

This application is a simple function generator, implemented on the official website, in the form of a VKontakte application.

There is also a generator widget to embed on your site.

The main difference from the previous described application is that this allows you to disable the repetition of the result.

That is, when conducting several generations in a row in one session, the number will not repeat.

• The presence of a widget to insert on a website or blog;
• Ability to disable the repetition of the result;
• The presence of the function "even more randomness", after the activation of which the selection algorithm changes.

Negative:

• The impossibility of determining several results at once;
• Inability to select from a specific list of numbers;
• To select a winner in public, you must use a separate VKontakte widget.

User reviews are as follows: “It works stably, it is quite convenient to use”, “Convenient functionality”, “I use only this service”.

Random number

<Рис. 5 Случайное число>

This service is located at http://random number.rf/.

A simple generator with minimum of functions and additional features.

Can randomly generate numbers within a given range (maximum from 1 to 99999).

The site does not have any graphic design, and therefore the page is easy to load.

The result can be copied or downloaded with the click of a button.

Negative:

• No widget for VKontakte;
• There is no possibility of holding draws;
• There is no way to insert the result into a blog or website.

Here is what users say about this service: “Good generator, but not enough functions”, “Very few features”, “Suitable for quickly generating a number without unnecessary settings.”

Randomus

<Рис. 6 Рандомус>

You can use this random number generator at http://randomus.ru/.

Another simple one, but functional random number generator.

The service has sufficient functionality for determining random numbers, however, it is not suitable for holding draws and other more complex processes.

Negative:

• The impossibility of holding draws based on post reposts, etc.
• There is no application for VKontakte or a widget for the site;
• It is not possible to disable repeating results.

With this generator you will be able to generate random numbers in any range. This generator will also allow you to randomly select or determine a number from a list. Or create an array of random numbers from 2 to 70 elements. This online tool will not only allow you to generate one (1), two (2) or three (3) digit random numbers, but also five and seven. Easy to set up. Everyone can master it. You will also be able to choose random numbers for online or offline lotteries or contests. And it will be convenient. You can easily create entire tables or rows of random numbers. In a fraction of a second, you will receive a random number or their sequence (set) on your screen. If you take a sequence of your numbers, then the algorithm will choose a random one or random ones, any one can fall out. You yourself can use this tool to conduct draws. By choosing, for example, the same range and number of numbers as a result, you can generate a random sequence (combination). You can also choose random letter combinations and words. This tool, like everything on our site, is absolutely free to use (no exceptions).

Enter range numbers

Changing the Range to Generate a Random Number

1..10 1..100 1..1000 1..10000 for lottery 5 out of 36 for lottery 6 out of 45 for lottery 6 out of 49 for lottery 6 out of 59

Number of random numbers (1)

Eliminate repetitions

Select random values ​​from the list (separate by commas or spaces, if commas are found, the division will be made by them, otherwise by spaces)

What is randomness in a computer? How is random number generation done? In this article, we have tried to give simple answers to these questions.

In software, and in technology in general, there is a need for reproducible randomness: numbers and pictures that seem random are actually generated by a certain algorithm. This is called pseudo-randomness, and we'll look at simple ways to generate pseudo-random numbers. At the end of the article, we formulate a simple theorem for generating these seemingly random numbers.

Determining what exactly is randomness can be quite a challenge. There are tests (Kolmogorov complexity, for example) that can give you an accurate measure of how random a given sequence is. But we will not bother, but simply try to create a sequence of numbers that will seem unrelated to each other.

Often, not just one number is required, but several random numbers generated continuously. Hence, given the initial value, we need to generate other random numbers. This initial value is called seed, and later we will see how to get it. For now, let's concentrate on generating other random values.

Generating random numbers from a seed

One approach might be to apply some crazy math formula to the seed, then twist it so much that the output number seems unpredictable, and then take that as the seed for the next iteration. The only question is what this distortion function should look like.

Let's experiment with this idea and see where it takes us.

The distortion function will take one value and return another. Let's call it R.

R(Input) -> Output

If the value of our seed is 1, then R will create a series of 1, 2, 3, 4, ... Looks not at all random, but we'll get to that. Now let R add a constant instead of 1.

If c equals, for example, 7, then we get a series of 1, 8, 15, 22, ... Still not right. Obviously, what we are missing is that the numbers should not only increase, they should be scattered over some range. We want our sequence to go back to the beginning - a circle of numbers!

number circle

Let's look at the clock face: our series starts at 1 and goes around to 12. But since we are working with a computer, let's put 0 instead of 12.

Now, starting from 1, we will add 7 again. Progress! We see that after 12 our series begins to repeat, no matter what number we start from.

Here we get a very important property: if our cycle consists of n elements, then the maximum number of elements that we can get before they begin to repeat is n.

Now let's rewrite the R function to fit our logic. You can limit the length of the loop using the modulus operator or the modulo operator.

R(x) = (x + c) % m

At this point, you may notice that some numbers are not suitable for c. If c = 4, and we started with 1, our sequence would be 1, 5, 9, 1, 5, 9, 1, 5, 9, … which of course doesn't suit us, because this sequence is absolutely not random. It becomes clear that the numbers we choose for the length of the cycle and the length of the jump must be related in a special way.

If you try several different values, you can see one property: m and c must be coprime.

So far we've been jumping by adding, but what if we use multiplication? Let's multiply X to a constant a.

R(x) = (ax + c) % m

The properties that a must obey in order to form a complete cycle are a little more specific. To create a valid loop:

1. (a - 1) must be divisible by all prime factors m
2. (a - 1) must be divisible by 4 if m is divisible by 4

These properties, together with the rule that m and c must be coprime, constitute the Hull-Dobell theorem. We won't go into the proof of it, but if you took a bunch of different values ​​for different constants, you could come to the same conclusion.

Seed selection

It's time to talk about the most interesting part: the choice of the initial seed. We could make it a constant. This can be useful when you need random numbers, but you want them to be the same every time you run the program. For example, creating the same map for every game.

Another way is to get a seed from a new source each time the program is started, just like in the system clock. This is useful when you need a total random number, like in a dice rolling program.

Final result

When we apply a function to its result multiple times, we get a recurrence relation. Let's write our formula using recursion.