Methods of random sampling by utilizing electronic sampler of random number
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National Standard of the People's Republic of China
Methods of random sampling by utilizingelectronic sampler of random number
Methods of random sampling by utilizingelectronic sampler of random numberSubject Content and Scope of Application
GB/T155001995
This standard specifies the method of obtaining random numbers and conducting simple random sampling by utilizingelectronic random number sampler. This standard is applicable to the sampling survey and product quality sampling inspection in various fields. 2 Reference Standards
GB10111—88 Methods of random sampling by utilizing electronic sampler of random number3 Terminology
3.1 Sampling: The process of randomly selecting or forming a sample. 3.2 Simple random sampling: From a population containing N individuals, select \ individuals so that all possible combinations containing \ individuals have equal probability of being selected.
According to the definition of simple random sampling, each unit (or unit product) in the population has equal probability of being selected into the sample. 3.3 Overflow: The displayed random number is larger than the total number or batch number N. 4 Symbol
N—the size of the total number or the batch number of the product;
n Sample size:
R—--·Random numbers obtained by an electronic random number sampler. 5 Electronic random number sampler and its use method 5.1 The electronic random number sampler is a random sampler composed of electronic devices such as a dedicated random number generator module, and its appearance is shown in Figure 1. Approved by the State Administration of Technical Supervision on January 4, 1995 and implemented on March 1, 1995
CB/T 15500—1995
Machine number
Figure 1 Electronic random number sampler
1—Power switch 2—Hundreds digit display screen, 3—Hundreds digit preset switch 14—+ digit display screen; 5—Tens digit preset switch; 6—Units digit display screen, 7—Units digit preset switch, 8—Random number extraction button 9—Shell 5.2 Random sampling procedure
Number the sampling units or unit products in natural numbers starting from \1\, and then use the obtained random numbers to extract the units. If the sampling units or unit products are not convenient to number, such as small components with a large batch size, you can also obtain random numbers, then count the components one by one, and extract according to the random numbers.
5.3 How to use the electronic random number sampler 5.3.1 Pre-stomach method of population size or batch size N There are two methods for pre-stomach method of population size or batch size N. Select one of them according to the value of N. 5.3.1.1 Method: The preset method according to the range of the total size or batch N is shown in Table 1. Table 1 Preset method according to the range of N
N range
11≤Ns99
101N999
N preset method
The hundreds and tens are reserved and reset to zero, the ones preset switch is set to N, the hundreds preset switch is set to zero, the tens preset switch is preset to the upper digit of N, the hundreds insert switch is preset, and the hundreds digit of N is preset in sections according to the number of digits of N; the preset method of each section is the same as GB/T 15500-1995
5.3.1.2 Method 2: When the total size or batch N is equal to AX10°, use the preset method of N minus 1. This method can ensure that the random number picked is less than or equal to the batch number N, and will not produce overflow greater than the batch number N. In the above formula, A1, 2, 3, 4, 5.6, 7.8.9, b--1, 2, 3, 4.5..*.--**
N—1 No overflow presetting method is shown in Table 2.
Table 2N--1 No overflow pre-masking method
N valuebZxz.net
10.20+30, 40, 50, 60.70, 80, 99, 100200, 300.400, 500, 600, 700, 800, 900, 10002000, 8000, 4000.5000.6000.7000.8000, 9000, 10C005. 3.2 Reading method of random number R
N—1 Presetting method
Hundreds digit preset switch is set, tens digit preset is set by pressing the tens digit of N minus 1 and then
Hundreds digit preset switch is set by pressing the hundreds digit of N minus 1 and then N is preset in sections. The preset method of each section is the same as that of 5.3.2.1: After the electronic random sampler presets the population or batch N using the method of 5.3.1.1, press the power switch to turn on the power. At this time, each time the random number extraction button is pressed, the display screen can display a random number R extracted. If 016 or R. 0 or repeated, this random number should be discarded and re-drawn. Example 3: N= 50, n=5
Because N=50=5×10, the N-1 overflow-free preset method can be used. Set the hundreds preset switch to zero and the tens preset switch to 4. Simply press the random number extraction button 5 times in succession to get 5 random numbers randomly drawn from N=50. For example: K,-34,R=26,R8,R=00.R,=44. Because R-00 means R=M, so R, take 50. A sample of 5 is formed. When the random number appears repeatedly, it should be discarded and re-drawn until a different random number is obtained.
Example 4: N=484, n=8
Set the hundreds digit preset switch to 4, and press the random number extraction button several times to get 8 random numbers randomly selected, for example, R=123, R2—482, R1, R,=88, R,-324, R,493.R,-88.R-18R—498>484, R,=88 5R are the same + so R and R should be discarded and re-extracted (for example, R=42, Rz=364). So the 8 random numbers randomly selected from N=484 are R,-123.R=482.R.=4,R=88,R.-324,R-42,R—364.R—18, which constitutes a sample of n=8. Example 5. N-=800,=13
Because N=800=8×10°. So N-1 no-out preset method can be used. GB/T 15500-1995
Preset the hundreds digit preset switch to 7, and just press the random number extraction button 13 times in a row to get 13 random numbers randomly extracted from the batch N=800. For example, R,=442, Rz284, R=6, R=17, R,-135, K,-713.R,=8, R=28R-637, R-735, R1=288R-465, R1=62 form a sample of 1=13. When the random number appears repeatedly, it should be discarded and re-extracted until the same random number is obtained.
Example 6: N-3468, n=20
Because N>1001, it is necessary to use the segmented preset method according to the number of digits in N. The random number R drawn from the first three digits for the first time, and R\ drawn from the last digit for the first time, are combined according to R=10R\+R\ to obtain the random number drawn from the batch N-3468. Because R is composed of R and R\ according to the above formula, when drawing R' or R\ respectively, the same random number does not need to be discarded. R'=000 or R\=0 does not need to be discarded. Only after R' and R\ are combined into R, opposite random numbers appear or R=000 and R\=0 appear at the same time, do you need to discard and re-draw. The specific method is as follows: When K is drawn from the first three digits for the first time, the hundreds digit is preset to zero. Draw 20 random numbers, for example: R-258, R=324, R,=56, R=291, Rs=392, R-.294, R=208, R=77, R=17, Rc=268R1=219R2-263, R=296, Ru281, Rs=162, Re-62, R1=279, R=131, Rg = 77, Ko=81. C is R,=392>316, so it should be discarded and re-drawn. If it is 246, then R:=246. When R\ is drawn from the undrawn digits for the second time, the hundreds digit and tens digit preset switches are all set to zero, and the ones digit preset switch is set to 9, which can also be preset, and 20 random numbers are drawn. For example: R\=2,R\=9.R\:6.R\=1,R\=9,R\-0,R\=5,R\=1R\=9,Rm\=0,R..\=6.R\-1,R3\-7,R\-8,R\-4,R\-9,R,\=3,R\\-2.R\-7.R\-3 Then press R=10R+R\ combination to get 20 random numbers randomly drawn from batch N=:3468: R,=2582, R=3249, R, - 566,R = 2911, R: = 2469. R 2940, R, = 2085, Ra - 771, R. = 179,R1 = 2680,Ru=2196,R12—2631,R=2967,R1.=2818,Rts=1621,Rs=629.R.2793,Re=1312,Rl=777.Ran813.
In this example, it can be seen that although R\= R77,K\=Rla\= 2,R\= R\=R\= R\= 9, but R\- 1,R.\=7, so R,=771 and R-777 are not the same, so when extracting R, although R,-R are the same, it is not necessary to discard and re-extract,
Example 7: N-60000,=32
Because N=60000=6×101, the N1 non-overflow preset method can be used. Divide the number of digits in N into segments and preset them in sections. For the first time, draw a random number R from the first three digits. For the second time, draw a random number R\ from the second digit. Combine R-100R' plus R\ to get the random number drawn from the batch N=60000. The specific method is as follows: when drawing R from the first digit for the first time, preset the hundreds digit preset switch to 5 and draw 32 random numbers. For example: R, a 477, R/-296.R=400,R=238,K-71,R=131,R=481,R*5,R-550,R=201,RI=324.R12=469,R,=307,R=486,R=228,R-287Ri=529,R=7l,Rs=85,Rz-484 ,K -246.R2=31,Ra-511,Rzt= 25,Rz-435,R2=265,Kz - 442,Kz 206,Rzg=330,Ro=242..1 =234,Rs2 -237.
When you draw R\ in the last digit for the second time, set the white digit preset switch to zero and the tens digit preset switch to 9. You don't need to preset, and draw 32 random numbers. For example. R,\=89,R\=61.R\=26,R.\-25,R,\=72,R\--81,R\=84,R\-18,R. \=76,R.\-- 60,R1\= 42, Rt\- 72, Ra\- 51, R.\= 84,Rs\- 41, R\= 81, Rw\= 23, R1\= 26, Rls\= 87.R2\=49,Rg\=57,R\=95,Kz\=33,R\=08,Rs\=56,R2\=65,R2\90,R\-61,Rz\r71Ry\- 58,Rs\=-23,Raz\= 96. Press R100R+R\ combination to get 32 random numbers randomly drawn from batch N-60000: R,=47789,Kz—29661,R= 40026,R, -- 23825,R.= 7172,R=13181,R, =48134,R, 518,R= 55076R=20160,.-32442,R=46972,R=30751.R48684.R.=22841.R-28781,R.52923R=7126.R=8587,K--48449,R=24657.Re=3195,R:--51133,Ru-250 8,R2e=43556GB/T15500
—1995
R—26565,R=44290,R2u-20661.Rag=33071,Rao=24258,R—23423,Ra—23796. In this example, it can be seen that although R=Rs=71, R\=R\=72, R\-R\—81, R\=R\=61, but R\=72, K.\一26, so Rs=7172, R=.7126 are not the same, so as in the above example, when drawing R' and R\ separately, the same random number does not need to be discarded. Only after R and R\ are combined into R, the same random number needs to be discarded and re-drawn. Additional explanation,
This standard is proposed by Jiangsu Provincial Bureau of Standards.
This standard is under the jurisdiction of the National Technical Committee for the Application of Statistical Methods. The drafting unit of this standard: China Institute of Standardization and Information Classification and Coding, Jiangsu Standard Technology Development Company. The main drafters of this standard are Kuo Jiyang, Liu Pingjun, Shou Zhenfan, Xu Shuning, and Yan Ruqin.
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