Random number table

A randomly generated number table consisting of ten numbers from 0 to 9

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zero

This entry is made by Compilation and application of scientific encyclopedia entries of "Science Popularization China" to examine.

Random number table, also known as random number table, is a number table composed of ten numbers randomly generated from 0 to 9. The number of times each number appears in the table is roughly the same, and the order in which they appear in the table is random.

The random number table is composed of random numbers generated by statisticians with computers, and ensures that the number appearing at each position in the table is of equal probability. Using the random number table to extract samples ensures that the probability of each individual being extracted is equal.

Chinese name: Random number table
Foreign name: random number table
Also called: Random number table

Appears: The order on the table is random Of
Adopt: Random number table method Sampling
Meaning: Non subjective

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brief introduction

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Random number table is a table randomly arranged (without any regularity) by numbers from 0 to 9. There are 2500 independent numbers in the table, which are arranged horizontally from left to right as rows and vertically from top to bottom as columns. There are many forms and usages of the table. When using the table, you can use several random numbers according to the number of individuals contained in the overall study object, that is, you can use it as any number as needed. The random number table method is a random sampling method that uses a random number table instead of a sign number or a sign cylinder. Its advantages are as follows: First, it is simple and feasible. Before sampling, only the research objects need to be numbered sequentially, and then they can be seated according to the randomly selected number; The second is the principle of "randomization" (the so-called "randomization" principle refers to the principle of "equal opportunity" in which every individual in the population has the same opportunity to be independently sampled into the sample during sampling. The sampling is accidental or not, which makes the sampled samples more representative.

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significance

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Random number table^[1]

The real random number is physical phenomenon Generated: such as coin toss dice Runner, use electronic component Of noise 、 Nuclear fission wait. Such random number generators are called physical random number generators. Their disadvantage is that their technical requirements are relatively high.

The random number table we usually use is Pseudorandom number , these series They are seemingly random numbers. In fact, they are generated by a fixed and repeatable calculation method. Random numbers generated by computers or calculators have a long periodicity. They are not really random, because they can actually be calculated, but they have statistical characteristics similar to random numbers.

use Random number table method Take samples, completely exclude the possibility of subjective selection of samples, so that the sampling survey is more scientific^[2] 。

step

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1. Unified numbering. That is to say, all the research objects in the overall study are numbered uniformly and signed. If the research object is within 10 and only one digit is taken, the number is 1-9; If the research object is between 1 and 99, take 2 digits, then the number is 01 to 99; If the research object is between 1 and 999, take 3 digits, then the number is 001 to 999; Others in turn. Then they are fully mixed to make the sample numbers evenly distributed, in line with the principle of "equal opportunity".

2. Determine the row name. According to their own needs or wishes, researchers can choose a line of numbers on the table, and the number of starting lines is determined by the line of numbers. If 25 lines are selected, the 25th line from top to bottom is the starting line. If the selected number is greater than 50, subtract 50 from the selected number, and the remainder is the starting line. If row 0 or row 00 is selected, row 50 is the starting line.

3. Determine the column name. The column name is determined in the same way as the row name.

4. Admission number. After the row and column names are determined, the number at the intersection of the selected number of starting rows and starting columns can be the starting point, and then the numbers can be recorded in a certain order direction (such as from left to right or from right to left, from top to bottom or from bottom to top). In case of numbers larger than the whole or repeated numbers, they should be rounded off, Until the number of samples taken is full. The number obtained by the above method is the sample selected at random^[3] 。

purpose

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For example, the ID and password of banks are very fragile. If there is a random number table, you can prevent such events. The random number table refers to assigning a different number list to each customer. When applying, the random number table is assigned to customers instead of being given according to certain rules, which is much safer.

For another example, to investigate the quality of a company's milk products, if you want to select 60 bags from 800 bags of milk, you can select a number from the random number table, and use the different reading methods of up, down, left, and right to form 60 numbers, and test according to the label of the milk. Although it is troublesome, it is often used.

Take a detailed example: an enterprise needs to investigate the demand of consumers for a product, and it needs to select 10 residents from 95 households by code table method. The specific steps are as follows: Step 1: number 95 households, one for each household, namely 01~95. (Number of each household is 2)

Step 2: In the above table, randomly determine the starting point and order of sampling. Assume that the sampling starts from the first row and the fifth column, and the sampling order is from left to right. (transverse series It is called "row", and the vertical sequence is called "column")

Step 3: Draw out 10 numbers in sequence: 86, 36, 96, 47, 36, 61, 46, 98, 63, 71. Since the numbers 96 and 98 are not in the overall number range, they should be excluded. Add two numbers: 62 and 74.

The resulting 10 sample unit numbers are: 86, 36, 47, 36, 61, 46, 63, 71, 62, 74.^{[4 ]}

The households with these numbers are the objects of sampling survey.

In real life, these random number tables play a very important role, so many people will specifically look for random number table generators.

program

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In C language, the rand() function can be used to generate random numbers, but it is not a real random number Pseudorandom number According to a number, we can call it seed Recursive formula The calculated coefficient, when the series number is large, conforms to the normal distribution, which is equivalent to generating a random number, but it is not a real random number. When the computer is turned on normally, the value of this seed is fixed, unless you destroy the system. In order to change the value of this seed, C provides the srand() function, whose original form is void srand (int a). Initialize the random generator, that is, the initial value of the rand() function, even if the value of the seed is changed to a; From this, you can see that through the srand() function, we can generate predictable random sequences. How can we generate unpredictable random sequences? We may often need such random sequences. Using srand ((unsign) (time (NULL)) is a method, because the time of running the program is different each time. Usage of random number generator provided in C language: current C compiler Both provide a ANSI Standard Of Pseudorandom number Generator function, used to generate random numbers. They are rand() and srand() functions. The working process of these two functions is as follows:

1) First, provide a seed for srand(), which is an unsigned int type with a value range from 0 to 65535;

2) Then call rand (), which will

3) Call rand () as many times as needed to obtain new random numbers without interruption;

4) At any time, you can provide a new seed for srand() to further“ randomization ”The output result of rand().

The following is a random number procedure between 0 and 32767:

#include < stdlib.h >

#include < stdio.h >

#Include<time. h>//Use the current clock as the seed

void main( void )

{int i;

srand( (unsigned)time( NULL ) ); // Initialize random number

for( i = 0; I<10; i++)//Print 10 random numbers

printf( " %d\n", rand() );

}

According to the above procedure, it is easy to get the random number between 0 and 1:

#include <stdlib.h>

#include <stdio.h>

#include <time.h>

main( )

{int i;

srand( (unsigned)time( NULL ) );

for( i = 0; i < 10;i++ )

printf( "%5.2f\n", rand()/32767.0);

}

The random number between 1 and 100 can be written as follows:

#include <stdlib.h>

#include <stdio.h>

#include <time.h>

main( )

{int i;

srand( (unsigned)time( NULL ) );

for( i = 0; i < 10;i++ )

printf( "%d\n", rand()%100+1);

}

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include <stdio.h>

#include <stdlib.h>

#include <time.h>

void main()

{

int i;

srand((unsigned)time(NULL));

i = rand() % 100;

}

The resulting random number is between 0-99,

The working process of these two functions is as follows:

1) First, provide a seed for srand(), which is an unsigned int type with a value range from 0 to 65535;

2) Then call rand(), which will return a random number (between 0 and 32767) based on the seed value provided to srand()

3) Call rand () as many times as needed to obtain new random numbers without interruption;

4) At any time, you can provide a new seed for srand() to further "randomize" the output results of rand().

#include <stdlib.h>

#include <time.h>

main

{

int i;

srand(time(0)); // Initialize random seed

i = rand(); // Generate random number

}

First, add a "# include<stdlib. h>

Then set a variable, such as j, j=rand(), and you can assign a random number of 1~32767 to j. If you want to get the ten digits of a random function (other similar), just make j=j/10 Add the header file # include<time. h>and then add srand ((unsigned) time (NULL)) to the file;

Srand() is used to initialize random Number of seeds Because the internal implementation of rand is done by linear congruence, it is not really a random number, but because its cycle is very long, it can be regarded as random in a certain range The above is a description and method of a random seed. To avoid repetition, use the random function rand(). The header file is stdlib.h

Random() generates a random number of 0 or 1

Random (n) generates a random number between 0 and n

Rand() generates a random number between 0 and 32768

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