The document explains census and sampling as methods for data collection from populations, highlighting the differences between them. Sampling involves selecting a subset of units from a population for study, and it can be categorized into probability and non-probability methods, with various techniques outlined such as simple random sampling, systematic sampling, stratified sampling, cluster sampling, and multi-stage sampling. Each method has its advantages and specific applications, emphasizing efficiency in time and cost while maintaining accuracy in data collection.

1. Sampling Methods and Distributions
Census versus Sampling
Census is the process of obtaining responses from/ about
each of the members of the population. The
determination of the size of the population of a
country is an example of census. This process is also
known as population census.
Sampling is a process of selecting a subset of randomised
number of members of the population of a study and
collecting data about their attributes. The limited
members of the population selected for sampling are
called as sampling units.

2. Advantages of Sampling
• Less time taken to collect data
• Less cost for data collection
• It is the only option while collecting data
• More accuracy of data collected due to its
limited size.
The size of the number of sampling units is
relatively smaller when compared to that of
the population, which results in reduced time
and cost of data collection

3. Notations of Parameters of Population and Sample
Measure Population Sample
Mean µ
Variance
Sample Size N n
Proportion P p
2

X
2
S

4. Sampling Frame
The complete list of all the members/ units of
the population from which each sampling unit
is selected is known as sampling frame. It
should be free from error. A perfect sampling
frame will contain its each unit only once. The
sampling frame must be complete, accurate,
adequate and up to date.

5. Sampling Methods
Sampling methods can be classified into probability sampling
and non-probability sampling methods.
In ‘probability sampling’, each unit of the population has a
probability of being selected as an unit of the sample. But
this probability varies from one method to another method
of probability sampling. This type of sampling is free from
biases.
In ‘non-probability sampling’, there may be instances that
certain units of the population will have zero probability of
selection, because judgment, biases and convenience of
the interviewers are considered to be the criteria for the
selection of sample units of such sampling.

6. Probability Sampling Methods
Methods of probability sampling are listed as
follows:
1. Simple random sampling
2. Systematic sampling
3. Stratified sampling
4. Cluster sampling
5. Multi-stage sampling

7. Simple random sampling
Let N be the number of units of the population: , be the number units
of the sample (n<N). There are two ways of performing simple
random sampling, viz., simple random sampling with replacement
of units and simple random sampling without replacement of units.
Simple random sampling with replacement: in this method of
sampling, each unit of the population has the equal probability of
being selected as an unit of the sample given by the following
formula:
The probability of selection of each unit = 1/N
This means that the first unit of the sample will be selected from the
population with a probability of 1/N. the selection of unit of the
sample can be done using either random number table.

8. Contd….
Simple random sampling without replacement: in this method of
sampling, each unit of the population has a varying probability of
being selected as an unit of sample given by the following formula:
The probability of selection of the first unit = 1/N
The probability of selection of the second unit = 1/ N-1
.
.
.
The Probability of selection of the nth unit = 1/ N – (n-1)

9. Systematic sampling
This is a special king of random sampling in which the selection of the first unit of the sample from the
population is based on randomisation. The remaining units of the sample are selected from the population
at a fixed interval of n, where n is the sample size.
Let the size of the population (N) be 800 and the sample size (n) be 40. the units of the sampling frame are
divided into n number of intervals based on the ratio of N/n, as shown below
Sampling interval width, I = N/n = 800/40=20
The sampling frame consist of units with serial numbers from 1 to 800. this range is divided into 40
intervals, viz., 1-20, 21-40, 41-60, ….., 760-780, 781 – 800, where the total number of intervals is equal to
the sample size.
Then a number from the first interval 1-20 is selected randomly and the unit of the population with this
serial number is treated as the unit of the sample. Let the randomly selected unit from the first interval of
the population be 12. then, the second unit of the sample is the unit in the population with serial number
32 which is obtained by adding 20 (sampling interval with, I) to 12. then each of the reaming units of the
sample can be obtained from the population in the same manner by adding 20 to the serial number of the
previous unit selected from the population.
As per these guidelines, the units of the population with serial numbers 52, 72, 92, ……, 772 and 792 are
treated as the third, fourth , fifth, …. 30th and 40th units of the sample respectively.

10. Stratified sampling
Stratified sampling is an improvised sampling over random
and systematic sampling. This sampling will have more
statistical efficiency. In this sampling method, the population
is divided into a specified set of strata such that the members
within each stratum have similar attributes but the members
between strata have dissimilar attributes. This means that
each stratum is homogeneous when compared to the
population.

11. Example (Stratified Sampling)
A survey is conducted to analyse the status of employment of the recently graduated batch of
students of a premier technological university. It is planned to conduct stratified sampling for this
study. So, the population which consists of different colleges is divided into three strata viz.
government colleges, aided colleges and self-financing colleges. Since, the regulations of AICTE
and the respective university ensure uniform standard of infrastructure and educational
standards, proportional stratified sampling is used for this study. The total number of engineering
colleges in the university is 200. the number of engineering colleges in the three categories, viz.
government, aided and self-financing are 20, 50 and 130, respectively. If the sample size is 20,
determine the number of colleges to be sampled from each category.

12. Cluster Sampling
Cluster sampling is a sampling technique in which the population
is divided into different clusters such that the members within
each cluster are dissimilar (heterogenous) in terms of their
attributes, but different clusters are similar to each other. This
lead to the inference that each cluster can be treated as a
small population which posses all the attributes of the
population. Hence, in cluster sampling, any one of the clusters
is randomly selected and all the units of that cluster are
selected (sampled) to arrive at inference about the
population.

13. Multi-stage sampling
In a large scale survey covering the entire nation/ subcontinent,
the size of the sampling frame will be too large which leads to
more time and cost of the study. In such study, multi-stage
sampling technique helps designing a smaller sampling frame
which will make the study practicable in terms of cost and
time.
The multi-stage sampling employs more than one stage to
sample the population depending upon the reality.
Consider the case of studying the requirement of chemical
laboratory equipments in all the colleges in a country by
CHEMEQUIP LTD. This study can be done using multi-stage
sampling, as explained in the next slide.

14. Contd..
Stage 1: In the first stage, the different states of the country are
sampled from each region using stratified sampling. The
country can be divided into different regions (strata), viz. east,
west, north and south. Here, it is assumed that the states
(sampling units) within each regions are dissimilar.
Stage 2: After selecting some states from each region in stage-I
based on the particulars of the stratified sampling, again one
can use cluster sampling to identify a district from each
selected state by assuming different districts of each state as
its clusters. Here, it is assumed that the districts of a state are
similar, but the colleges in each district are dissimilar in terms
of their present chemical laboratory facilities.

15. Contd..
Stage 3: In each selected district, a random sampling
may be used to select the proportionate number of
colleges (sampling units) from it.
This study involves three stages of sampling. The
highest level of sampling units are states and the
lowest level of sampling units are colleges. From this
example, one can visualize the fact that the multi-
stage sampling reduces the size of the overall
sampling frame.