Stat Trek

Teach yourself statistics

Teach yourself statistics

# Random Number Generator

Use the Random Number Generator to create a list of random numbers (up to 10,000 numbers), based on your specifications. The numbers you generate appear in the Random Number Table.

For help in using the Random Number Generator, read the Frequently-Asked Questions or review the Sample Problems.

• Enter a value in each of the first three text boxes.
• Indicate whether duplicate entries are allowed in the table.
• Click the Calculate button to create a table of random numbers.
 How many random numbers? Minimum value Maximum value Allow duplicate numbers True False Seed (optional) None 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Note:  A seed value of "None" produces new random numbers with each computation. Any other setting produces the same random numbers, until the seed value is changed. The seed allows you to recreate the same random number table time after time.

## Random Number Table

100 Random Numbers
26500 29473 22649 80591 63105 40290 53307 24284 50021 50563 34428 70108 69993 43305 23217 27690 50398 67645 78544 01674 33549 27883 93751 93286 72017 97563 54462 26899 48937 58526 21402 01591 23325 64977 38206 67709 00386 32548 64229 28433 26831 52358 32364 66338 11187 30076 31850 94956 69109 49987 16087 35336 93694 64050 35446 17614 50793 05962 95086 07565 99322 30221 37762 58175 36579 76190 51639 86198 68551 57155 03105 73720 05229 74392 94583 94721 80921 56227 47343 66640 99563 22101 09317 26934 05035 71628 87908 34641 76468 98662 07806 96947 48560 30359 93795 20741 56890 91235 78573 89184
Specs: This table of 100 random numbers was produced according to the following specifications: Numbers were randomly selected from within the range of 0 to 99999. Duplicate numbers were allowed. This table was generated on 9/29/2023.

Instructions: To find the answer to a frequently-asked question, simply click on the question.

### What are random numbers?

Random numbers are sets of digits (i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) arranged in random order. Because they are randomly ordered, no individual digit can be predicted from knowledge of any other digit or group of digits.

### What is a random number generator?

A random number generator is a process that produces random numbers. Any random process (e.g., a flip of a coin or the toss of a die) can be used to generate random numbers. Stat Trek's Random Number Generator uses a statistical algorithm to produce random numbers.

### What is a random number table?

A random number table is a list of random numbers. Stat Trek's Random Number Generator produces a list of random numbers, based on the following User specifications:

• The quantity of random numbers desired.
• The maximum and minimum values of random numbers in the list.
• Whether or not duplicate random numbers are permitted.

### How "random" is Stat Trek's Random Number Generator?

Although no computer algorithm can produce numbers that are truly random, Stat Trek's Random Number Generator produces numbers that are nearly random. Stat Trek's Random Number Generator can be used for most statistical applications (like randomly assigning subjects to treatments in a statistical experiment). However, it should not be used to generate numbers for cryptography.

### What are the minimum and maximum values in the Random Number Generator?

The minimum and maximum values set limits on the range of values that might appear in a random number table. The minimum value identifies the smallest number in the range; and the maximum value identifies the largest number. For example, if we set the minimum value equal to 12 and the maximum value equal to 30, the Random Number Generator will produce a table consisting of random arrangements of numbers in the range of 12 to 30.

### What does it mean to allow duplicate entries in a random number table?

Stat Trek's Random Number Generator allows Users to permit or prevent the same number from appearing more than once in the random number table. To permit duplicate entries, set the drop-down box labeled "Allow duplicate numbers" equal to True. To prevent duplicate entries, change the setting to False.

Essentially, allowing duplicate entries amounts to sampling with replacement; preventing duplicate entries amounts to sampling without replacement.

### What is a seed?

The seed is a number that controls whether the Random Number Generator produces a new set of random numbers or repeats a particular sequence of random numbers. If the dropdown box labeled "Seed" is set to "None", the Random Number Generator will produce a different set of random numbers each time a random number table is created. On the other hand, if a number is selected for "Seed", the Random Number Generator will produce a set of random numbers based on the value of the Seed. Each time a random number table is created, the Random Number Generator will produce the same set of random numbers, until the Seed value is changed.

Note: The ability of the seed to repeat a random sequence of numbers assumes that other User specifications (i.e., quantity of random numbers, minimum value, maximum value, whether duplicate values are permitted) are constant across replications. The use of a seed is illustrated in Sample Problem 1.

Warning: The seed capability is provided for Users as a short-term convenience. It allows a User to regenerate the same set of random numbers tomorrow as he/she generated today. However, there is a risk to relying on the seed capability to recreate a particular random number table. From time to time, Stat Trek may change the underlying random number algorithm to more closely approximate true randomization. A newer algorithm will not reproduce random numbers generated by an older algorithm, even with the same seed. Therefore, the safest way to "save" a random number table is to print it out. The algorithm was last changed on 3/11/2022.

## Sample Problem

1. A university is testing the effectiveness of two different medications. They have 10 volunteers. To conduct the study, researchers randomly assign a number from 1 to 2 to each volunteer. Volunteers who are assigned number 1 get Treatment 1 and volunteers who are assigned number 2 get Treatment 2. To implement this strategy, they input the following settings in the Random Number Generator:

• They want to assign a number randomly to each of 10 volunteers, so they need 10 entries in the random number table. Therefore, the researchers enter 10 in the text box labeled "How many random numbers?".
• Since each volunteer will receive one of two treatments, they set the minimum value equal to 1; and the maximum value equal to 2.
• Since some volunteers will receive the same treatment, the researchers allow duplicate random numbers in the random number table. Therefore, they set the "Allow duplicate entries" dropdown box equal to "True".
• And finally, they set the Seed value equal to 1. (The number 1 is not special. They could have used any positive integer.)

Then, they hit the Calculate button. The Random Number Generator produces a Random Number Table consisting of 10 entries, where each entry is the number 1 or 2. The researchers assign the treatment indicated by the first entry to volunteer number 1, the treatment indicated by the second entry to volunteer number 2, and so on.

Using this strategy, what treatment did the first volunteer receive? What treatment did the tenth volunteer receive?

Solution:

This problem can be solved by recreating the exact Random Number Table used by the researchers. By inputting all of the same entries (especially the same Seed value) that were used originally, we can recreate the Random Number Table used by the researchers. Therefore, we do the following:

• Enter 10 in the text box labeled "How many random numbers?".
• Set the minimum value equal to 1 and the maximum value equal to 2.
• Set the "Allow duplicate entries" dropdown box equal to "True".
• Set the Seed value equal to 1.

Then, we hit the Calculate button. This produces the Random Number Table shown below.
10 Random Numbers
1 1 1 2 2 1 1 2 1 2
Specs: This table of 10 random numbers was produced according to the following specifications: Numbers were randomly selected from within the range of 1 to 2. Duplicate numbers were allowed. This table was generated on 9/29/2023.
From the table, we can see that the first entry is "1". Therefore, the first volunteer received Treatment 1. And the second entry is also "1". Hence, the second volunteer also received Treatment 1. And so on. The tenth volunteer received the tenth number in the list, which is "2". So the tenth volunteer received Treatment 2.
1. We would like to survey 500 families from a population of 20,000 families. Each family has been assigned a unique number from 1 to 20,000. How can we randomly select 500 families for the survey?

Solution:

We input the following settings in the Random Number Generator:

• We want to select 500 families. Therefore, we enter 500 in the text box labeled "How many random numbers?".
• Since each family has been assigned a number from 1 to 20,000, we set the minimum value equal to 1; and the maximum value equal to 20,000.
• Since we only want to survey each family once, we don't want duplicate random numbers in our random number table. Therefore, we set the "Allow duplicate entries" dropdown box equal to "False".

Then, we hit the Calculate button. The Random Number Generator produces a Random Number Table consisting of 500 unique random numbers between 1 and 20,000. We will survey the families represented by these numbers - a sample of 500 families randomly selected from the population of 20,000 families. ## Problem?

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