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# Simple Random Sample

A simple random sample is an unbiased surveying method where a subset of individuals is randomly selected from a larger population set, such that each individual has an equal probability of being selected at any given stage of the sampling process.  This process of selecting is known as simple random sampling.

The simple random sampling is a basic sampling which can be a part of other sampling methods.

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## Process of Selecting a Simple Random Sample

There are many ways to select a simple random sample.  One method is to use a lottery.  We can do it the following way.
Step 1: Identify the N number of units in the population and number them from 1 to N.

Step 2: Choose numbers randomly.  (one can make use of a random number table or draw a lottery)

Step 3: Choose the unit with the number you got randomly.

Step 4: Repeat from step 2. Make sure that if a number is repeated in the random number ignore and try again.
Selection can also be done using Algorithms and there exist several efficient algorithms which have been developed over the years.  Fan et al. in 1962 developed the selection-rejection algorithm, this was a sequential algorithm which needed to know the count of the items N and has to make a single pass over the data. In 1977 Sunter proved a very simple random sort Algorithm which assigns a unique random number as the key for each item, these random numbers are drawn from the uniform distribution (0,1), based on the key the set is sorted and the smallest k elements are selected. In 1985 Vitter, J. Proposed reservoir sampling algorithm which is widely used as it doesn’t depend on the count of the items.

Let us take an example to understand how a simple random sample can be obtained.  In a class, there are 50 students from them a sample of 20 is to be selected randomly. Now in this situation selection of each student is equally likely. To get a simple random sample we randomly give each person a number. Now they are numbered 1 to 50 in a random sequence. We put 50 numbers into a bag and draw randomly and not replacing the numbers drawn we should be able to find 20 students in a random manner. This is one way a simple random sample be obtained. To do it differently, any one of the above algorithms would be helpful.