# Application of Random Numbers

There are many uses of random numbers in statistics. One of the more important uses is in the selection of a simple random sample from a finite population. Suppose there are 80 students in a class and we want to select 8 students at random. The students can be numbered from 01 to 80. Then we consult the random number table.

Let us look at Table 8.1. We shall read the two–digit column. If any number is between 01 and 80, we shall note it down for the sample. If any random number is above 80, we shall ignore it because it is not in our population. We can read the random number table from any place. We may move column–wise or row–wise. Let us read the random numbers from Table 8.1 from the first column. The random numbers are *51, *72, 57, 38, 22,.45, 18, 69. Two random numbers 92 and 95 have been ignored because they are above 80. The remaining eight random numbers represent those eight students who have been selected for the sample. If the number of units in the population is in hundreds, say 800 we shall read the three–digit column of the random number table. If we have 100 units in the population, we shall number them from 00 to 99 so that we have to read the two-digit column. If we number them as 001, 002 … 100, we shall have to read the three–digit columns. In the three-digit column, most of the random numbers will be above 100 and a lot of time will be wasted in getting the required size of the sample. Further use of the random number table for the selection of a simple random sample will be discussed in sampling.

The random number table can also be used to generate data without performing the actual experiment. Suppose we want to toss a coin 10 times to see the number of heads. We can do it by:

**(i)** Tossing the coin and counting the number of heads.

**(ii)** By using a random number table. The even digits 0, 2, 4, 6, 8 will stand for heads and the odd digits 1, 3, 5, 7, 9 will be for tails. The first ten digits of the first row of the previous table are reproduced below. **H** is for heads and **T** is for tails.

Digits |
5 |
1 |
2 |
2 |
0 |
9 |
1 |
2 |
7 |
2 |

Outcomes |
T |
T |
H |
H |
H |
T |
T |
H |
T |
H |

There are 5 heads and 5 tails. It is just a chance that number of heads is equal to the number of tails. If we read the next row, the result in general would be different.

This process of getting the results of an experiment from a random number table is called simulation. In simulation the actual experiment is not performed.