A table of random digits is very helpful in the practice of statistics. Random digits are particularly useful for selecting a simple random sample.

### What Is a Table of Random Digits

A table of random digits is a listing of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. But what sets any listing of these digits apart from a table of random digits? There are two features of a table of random digits. The first property is that every digit from 0 to 9 is just as likely to appear in every entry of the table.

The second feature is that the entries are independent of each other.

These properties imply that there is no pattern to a table of random digits. Information about some of the table will not help at all to determine the other entries of the table.

For example, the following string of digits would be a sample of a part of a table of random digits:

9 2 9 0 4 5 5 2 7 3 1 8 6 7 0 3 5 3 2 1.

For convenience, these digits can be arranged in rows of blocks. But any arrangement is really just for ease of reading. There is no pattern to the digits in the above row.

### How Random?

Most tables of random digits are not truly random. Computer programs can produce strings of digits that appear to be random, but actually, have some sort of pattern to them. These numbers are technically pseudo-random numbers. Clever techniques are built into these programs to hide the patterns, but these tables are actually nonrandom.

To truly generate a table of random digits, we would need to convert a random physical process into a digit from 0 to 9.

### How Do We Use a Table of Random Digits

While a list of digits might hold some sort of visual aesthetic, it would be appropriate to ask why we care about tables of random digits. These tables can be used to select a simple random sample.

This kind of sample is the gold standard for statistics because it allows us to eliminate bias.

We use a table of random digits in a two-step process. Begin by labeling items in the population with a number. For consistency, these numbers should consist of the same number of digits. So if we have 100 items in our population, we can use the numerical labels 01, 02, 03, ., 98, 99, 00. The general rule is that if we have between 10^{N – 1} and 10^{N} items, then we can use labels with N digits.

The second step is to read through the table in chunks equal to the number of digits in our label. This will give us a sample of the desired size.

Suppose we have a population of size 80 and want a sample of size seven. Since 80 is between 10 and 100, so we can use two digit labels for this population. We will use the line of random numbers above and group these into two-digit numbers:

92 90 45 52 73 18 67 03 53 21.

The first two labels do not correspond to any members of the population. Selecting members with labels 45 52 73 18 67 03 53 is a simple random sample, and we could then use this sample to do some statistics.