A random number table is a grid of digits where every number from 0 to 9 appears with equal probability, and no number is influenced by the ones around it. You use it to pull a truly unbiased sample from a population by matching digits in the table to numbered members of your group. The process is straightforward once you understand a few core rules.
How the Table Works
A random number table is typically a large block of digits arranged in rows and columns. The digits satisfy two properties: every digit from 0 to 9 is equally likely to appear, and each digit is completely independent of those before and after it. This independence is what makes the table useful for sampling. You’re not picking favorites or following a pattern. You’re letting pure chance do the selecting.
The most famous example is RAND Corporation’s “A Million Random Digits,” originally produced for the United States Air Force and still considered the largest known source of random digits. It became a standard reference across engineering, economics, polling, quality control, and any field that relies on Monte Carlo simulations. Today, computers generate pseudo-random numbers for most applications, but physical tables remain a common teaching tool in statistics courses and are still used in fieldwork where computers aren’t practical.
Step-by-Step Process
Here’s the full procedure, from setup to final sample.
1. Number every member of your population. Assign a unique number to each person, item, or unit in your population, starting from 1 (or 001, 0001, depending on the size). If you have 85 people, number them 01 through 85. If you have 185, number them 001 through 185. If you have 4,000, number them 0001 through 4000.
2. Determine how many digits you need. This is the key step most people get wrong. Count the digits in your largest population number. A population of 85 is a two-digit number, so you’ll read two digits at a time from the table. A population of 185 is three digits, so you read three at a time. A population of 4,000 means you read four digits at a time. This digit count stays the same throughout the entire selection process.
3. Pick a random starting point. Close your eyes and point to a spot on the table. This sounds informal, but it’s the standard method taught in statistics. The goal is to avoid consciously choosing a “nice-looking” spot, which would introduce bias. Some people use the current time on a clock to pick a row and column. Either way, the starting point should not be deliberate.
4. Choose a direction and stick with it. Before you begin reading numbers, decide whether you’ll move down the column, across the row left to right, or across right to left. You can even flip a coin to decide. The direction itself doesn’t matter, but consistency does. Once you pick a direction, follow it until you’ve filled your sample.
5. Read your first number. Starting at your chosen spot, read the appropriate number of digits. For a population of 185, you’d read three digits. If the table entry at your starting point is 20631, you read the first three digits: 206.
6. Check if the number falls within your population range. Does anyone in your population have the number 206? If your population only goes up to 185, the answer is no. Skip it and move to the next entry in your chosen direction.
7. Keep going until you have enough. Continue reading numbers in sequence, skipping any that fall outside your population range. Also skip any duplicates, since you typically want each member selected only once. Record every valid number until you’ve reached your desired sample size.
8. If you hit the end of the table, pick a new random starting point, choose a new direction, and continue until you have all the numbers you need.
A Concrete Example
Say you have 185 students numbered 001 to 185, and you need a sample of 5. Since 185 is a three-digit number, you’ll read three digits at a time from the table.
You close your eyes, point, and land on the entry 20631. The first three digits give you 206. No student has that number, so you skip it. The next entry down is 89990, which gives you 899. Still out of range. You continue to the top of the next column and work down until you hit 10005, which reads as 100. Student 100 is your first selection.
Continuing in the same direction, you find four more valid numbers: 049, 082, 153, and 164. Those five students are your random sample.
Notice how many entries you had to skip. That’s normal, especially when your population size doesn’t neatly fill the digit range. A three-digit read gives you numbers from 000 to 999, but your population only goes to 185. Roughly 80% of numbers will be out of range. This is expected, not a sign you’re doing something wrong.
Reading Across vs. Reading Down
Researchers use different conventions for moving through the table. Some read down columns, others read across rows. Some use the first three digits of each entry, while others use the last three. All of these approaches are valid as long as you decide before you start and don’t switch mid-process. Changing your method partway through opens the door to unconscious bias, where you might gravitate toward numbers that “feel” right.
In field research, scientists sometimes need to generate coordinates rather than select people. The same principle applies. You might read three digits for an x-coordinate, then switch to a new starting point and read three digits for a y-coordinate. The table doesn’t care what the numbers represent. It just supplies the randomness.
Common Mistakes to Avoid
The most frequent error is choosing your starting point deliberately. If you always start at the top-left corner or pick a spot because the numbers “look random,” you’ve defeated the purpose. The blind-point method exists precisely to prevent this.
Another mistake is changing direction or skipping entries because a number seems too close to one you’ve already picked. If the table gives you student 100 and then student 101, both are valid selections. Randomness sometimes produces clusters, and overriding that pattern introduces bias.
Forgetting to skip duplicates is also a problem. If you’re sampling without replacement (the usual case), and the number 082 comes up twice, you only count it once and keep reading for an additional valid number.
Finally, using too few or too many digits per read is a structural error. If your population is 85 people and you read three digits at a time, you’ll waste enormous amounts of the table skipping numbers between 086 and 999. If your population is 185 and you only read two digits, you’ll never select anyone numbered 100 or above. Always match your digit count to the number of digits in your largest population number.
Random Number Tables vs. Computer Generators
Most modern research uses computer-generated random numbers instead of physical tables. These are faster and can produce millions of values in seconds. However, all algorithm-based generators are technically “pseudo-random,” meaning they follow a deterministic formula and will eventually repeat. For most practical purposes this repetition cycle is so long it doesn’t matter, but in very large simulations, the correlations that creep in can distort results by inflating variance between runs.
Physical tables, like RAND’s million-digit publication, were generated from electronic noise and don’t have this repetition problem. Quantum random number generators represent the newest approach, producing numbers from genuinely unpredictable quantum processes. For a classroom assignment or a small field study, though, a printed random number table works perfectly well and has the added benefit of being completely transparent: anyone can trace exactly which numbers you selected and verify your sample.