# Simple random sampling types and characteristics

Want to know about Simple Random Sample (SRS)? This article gives the basic information regarding SRS and its types as well as characteristics of each.

The simple random sample is basically of two types- Sampling with replacement (srs) and Sampling without replacement (srswor). These two topics are discussed here along with their characteristics.

## Simple Random Sample

### 1.1 Introduction

This is the most simple method of a sample survey. In this method, n units are selected as the sample from N populations one by one. Selection of a unit is done with the help of random number tables which we will discuss at the end of this articles.

### 1.2 Types of Simple Random Sample (srs)

There are two types of srs :a) Sample Random Sample with replacement (srswr).

b) Sample Random Sample without replacement (srswr).

### 1.2(a) Sample Random Sample with replacement (srswr)

A sample is said to be srswr if it follows the following conditions

i) The probability of each unit being selected at a particular draw is same.

i.e., p(e) = 1\N

e = event of selecting ith unit.

i= 1,2, ..... ,n.

ii) The selected unit is returned to the population before the next draw.

### Characteristics of srswr

* In srswr sample mean is an unbiased estimator of population mean .

* Variance of a sample mean is given by

* In srswr unbiased estimator of var() is given by

### 1.2(b) Sample Random Sample without replacement (Ssrswor)

A sample is said to be srswor if it follows the following conditions

* The probability of each unit being selected at a particular draw is same.

i.e., p(e)= 1\N

e = event of selecting ith unit,

i = 1,2,.....,n.

* The selected unit is not returned to the population before the next draw.

## Characteristics of srswor

* Probability of an unit is included in the sample from a population is n/N.

* In srswor sample mean is an unbiased estimator of population mean .

* Variance of sample mean is given by

* In srswor unbiased estimator of var() is given by

### Random Number Table

Selection of a unit is done with the help of random number tables. These are tables consisting of random numbers generated by some devices. Generally, these random numbers are between 0 to 9 occurring with equal frequencies.

There are many random number tables available, some of them are:

i) Tippet's random number tables.

ii) Fisher and Yates' random number tables.

iii) Random number tables prepared by Rand Corporation.

DiamondPoints : 4