Draw a random sample (without replacement) of 20 students from a class of 400 students.

Question:

Draw a random sample (without replacement) of 20 students from a class of 400 students.

Solution:

At the outset, identify the 400 students with numbers from 1 to 400. Now put your pencil edge with closed eyes on any number and then we pick out one by one on the three digited numbers less than or equal to 400, till 20 numbers from 400 are obtained. In this process the numbers over 400 are discarded and the repeated numbers, if any, are taken only once.

The above numbers grouped in three’s will be as below

295 266 413 992 979 279 795 911 317 056 244 167 952 415 451 396 720 353 561 300 269 323 707 483 340 827 623 563 108 969 137 691 056 052 461 112 610 760 088 126 423 387 762 754 914 314 059

The desired sample of 20 students will be constituted by the students corresponding to the ramdom numbers given below:

295 266 279 056 244 167 396 300 269 323 340 108 137 052 112 088 126 387 314 059

The use of random numbers in simple random sampling is quite practicable in case the size of population is limited and the sampling units not scattered over a large area. However, when the size of sampled population is quite large, listing of items itself and then using the random numbers would become a very time consuming and costly job.