The document discusses census and sampling methods in statistical data collection, noting the importance of identifying a population before selecting samples. It compares the census method, which involves complete enumeration, with the sample method that assesses a subset of the population, outlining their merits and demerits. Various types of sampling methods, including probability and non-probability sampling, are also explored, highlighting the need for representative and reliable samples to minimize statistical errors.

1. Chapter - 3
Census and
Sample Methods

2. Introduction
● We have seen in the previous chapter that
statistical tools are used in studying the
economic problems of a country.
● These tools help in studying and analyzing
various aspects of a given economic problem.
● Collection of data and methods used to collect
data are the initial steps towards analysing and
comprehending various economic issues.

3. ● In Statistics, universe or population simply
refers to an aggregate of items to be studied
for an investigation.
● In Statistics, the term population means the
aggregate of all items about which we want to
obtain information.
● A population refers to all the individuals/items
who possess certain characteristics according
to the purpose of the survey.
● The first task in selecting a sample is to
identify the population.
● Population is the area or subject matter of
statistical enquiry.

4. Methods of Statistical Enquiry
● There are two methods of statistical
enquiry.

5. (I) Census Method
● Census method is that method in which data
are collected covering every item of the
universe or population relating to the problem
under investigation.
● It is also known as the ‘Method of Complete
Enumeration’ or ‘100% Enumeration’.
● The essential feature of this method is that it
covers every individual unit in the entire
population.
● Census method implies complete enumeration
of the universe/ population.

7. Suitability
(1) Small size of population.
(2) Widely diverse items in the population.
(3) Requirement of extensive examination of
diverse items.
(4) High degree of accuracy and reliability.
(5) Selection of sample items from universe is
not possible.
Merits
(1) Reliable and Accurate: Results based on
census method are accurate and highly reliable.
This is because each and every item of the
population is studied.

8. (2) Less Biased: Since census method does not
involve investigator’s discretion regarding
selection of samples from the universe, there
are less chance of data collected being biased.
(3) Extensive Information: Census method
involves collection of meaningful exhaustive
information as all items of the universe are
studied.
(4) Complex investigations: When items in
population are diverse and complex and it is
essential to study each item separately, census
method is suitable and will give desired results.

9. (5) Indirect Investigation: Indirect
investigations on studies like poverty,
unemployment, brain-drain, corruption etc.
require data collection by census method.
Demerits
(1) Costly: Census method is very costly and is,
therefore, generally not used for ordinary
investigations. Only the Government or some big
institutions can afford to use this method.
(2) Large Manpower: Census method requires
lot of manpower. Training of a large number of
enumerators becomes essential, which is a very
difficult process.

10. (3) Not Suitable for Large Investigations: It
may become difficult to cover each and every
item if items under universe are large in number.
(4) Not universally operative: Census method
cannot be adopted if the population is infinite,
i.e., the one which is continuously changing.

11. (II) Sample Method
● Sample method is that method in which data
is collected about the sample on a group of
items taken from the population for
examination and conclusions are drawn on
their basis.
● A sample refers to a group or section of the
population from which data are obtained.
● A good sample is:
• smaller than population
• capable of providing reasonably accurate
information about population at a much lower
cost and shorter time.

13. Suitability
(1)The size of population is very large.
(2)Very high degree of accuracy is not needed.
(3) Extensive examination of diverse items is not
required.
(4) When different units of the universe are
broadly similar to each other.
(5) When census method is not applicable.
Merits
(1) Economical: Sample method of investigation
is economical because only some units of the
population are studied.

14. (2) Time Saving: In this method, only limited
numbers of the items are investigated,
therefore this process of investigation is time
saving, not time-consuming.
(3) Large Investigations: Sample method is
more feasible in situations of large
investigations than the census method which
generally involves unaffordable cost.
(4) More Scientific: According to R. Fisher,
Sample Method is more scientific because the
sample data can be conveniently investigated
from various angles.

15. Demerits
(1) Partial: It is only a partial investigation of
the universe. The investigator’s bias in the
selection of the sample is not ruled out.
(2) Wrong Conclusions: If the selected sample
does not represent the characteristics of the
universe, the study may end up with wrong
conclusions.
(3) Difficulty in Selecting Representative
Sample: It is not very easy to select a sample
which would represent the characteristics of
the entire population.

16. (4) Specialised Knowledge: Sampling involves a
set of technical procedures. One must have the
technical knowledge of choosing a representative
sample from the universe.

17. Difference between Census &
Sample Method
Basis Census Method Sample Method
1.Meaning
2.Coverage
3. Suitable
4.Accuracy
5. Cost
6. Time
7. Nature
of items
8. Skills
9.Verificat
on
Data are collected
covering every item of the
universe.
Covers the whole universe.
When area is limited or
small.
High degree of accuracy.
High in cost.
Time consuming.
Widely diverse items.
Needs more organisational
skills.
Verification is not
possible.
Data are collected about the
sample on a group of items
taken from the population.
Only a part of universe is
covered.
When area is wide or large.
Low degree of accuracy.
Low in cost.
Time saving.
Homogenous items.
Needs less organisational
skills.
Verification is possible.

18. Methods of Sampling

19. I. Probability Sampling Methods
● These are the methods in which every item in
the universe has a probability (known chance)
of being selected as a sample.
● These methods are further subdivided as
Unrestricted and Restricted Random
Sampling.
Probability
Sampling Methods
Unrestricted
Random
Sampling
Restricted
Random
Sampling

20. (A) Simple Random Sampling/Unrestricted
Sampling
● Random sampling is that method of sampling in
which each and every item of the universe has
equal chance of being selected in the sample.
● In other words, there is an equal probability for
every item of the universe being selected in the
sample.
● This method is used particularly when various
items of the universe are homogeneous or
identical to each other.
● Selection of items is beyond the control of
investigator.
● This method is impartial and economical.

21. ● It is a scientific method of sample selection and
not the haphazard selection of items.
● There are two ways of doing simple random
sampling.

22. (i) Lottery Method: Under lottery method, chits
or paper slips are made for each item in the
population. Then the chits are shuffled in the
container and without any biasness, some slips are
drawn out. The chits then become the samples of
the universe.

23. (ii) Tables of Random Numbers: Tippet has
prepared a table consisting of 10400 numbers of
four digits. In this method, all the items are
arranged in an order and using Tippet’s table,
required number of items are selected. This
method is also known as Tippet’s method.
Merits
(1) Free from bias- This method is impartial
and is free from personal bias of the
investigator.
(2) Equality- Each and every item of the
universe stands equal chances of being selected
as a sample. This ensures that the method is
impartial.

24. (3) Representative of the population- The
sample items fairly represents the universe. As
the size of random sample rises, it becomes more
representative of the population.
(4) Simple- Random sampling method is a simple
method and is convenient to use.
Demerits
(1) No proportionate representation - Random
sampling method does not ensure proportionate
representation of different items that
constitute the population.
(2) Ignores important items- This method does
not give weightage to important items in the
population.

25. (B) Restricted Random Sampling
● Simple Random Sampling method is suitable
when items of the universe are homogeneous.
● In the cases where different items of the
universe are heterogeneous, samples are
selected under some restrictions (based on
certain divisions).
(i) Stratified/ Mixed Sampling
● This method of sampling is generally adopted
when population consists of different groups
with different characteristics

26. ● According to this method of sampling,
population is divided into different strata having
different characteristics and some of the items
are selected from each strata, so that the
entire population gets represented.
● Stratified sampling is also known as mixed
sampling because it is a mixture of purposive
sampling (division of population into different
strata) and random sampling (selection of items
from different strata done randomly).
● It is important to ensure that each stratum is
represented in the correct proportion in the
sample.

28. Merits
(1) Covers diverse characteristics
(2) Representative- More representative
samples are obtained because the universe is
divided into strata and every stratum gets a
representation in the sample.
(3) Accuracy- This method ensures accuracy as
the variation among different strata reduces to
a great extent.
(4) Administrative convenience- Division of
universe into certain homogeneous strata and sub
strata ensures administrative convenience.

29. Demerits
(1) Limited scope- This method has a limited
scope as it requires complete knowledge regarding
diverse characteristics of the population.
(2) Biased- There may be biasness while
classifying different items of the universe into
different strata.
(3) Expensive- If the stratified samples are
distributed widely geographically, then it becomes
an expensive method of sample collection.
(4) Difficult if size of population is small- If
the size of the universe is already small, it
becomes difficult to divide the items into even
smaller strata.

30. (ii) Systematic Sampling
● Method in which out of the complete list of
available population, every nth item of the
numbered items is selected as a sample item is
called Systematic Sampling.
● This method is considered to be a short cut
method of Random Sampling.

31. Merits
(1) Simple- This method is simple and convenient to
use as compared to other methods of random
sampling or stratified sampling.
(2) Not biased- There exists no possibility of
personal bias by the investigator as every nth item is
selected as a sample item.
(3) Less Time consuming- Sampling by this method
involves less efforts and hence it is less time
consuming.
(4) Satisfactory conclusions- The conclusions
drawn by this method are satisfactory when periodic
features associated with sampling interval are not
present.

32. Demerits
(1) Unfair- Since every item in the universe does
not get equal chances of being selected, except
only the first item that is selected randomly, this
method becomes unfair.
(2) Misleading results- If periodic features
associated with sampling intervals are present the
results so obtained may not serve the purpose.
(3) Unsuitable if size of universe is large- This
method is not suitable when the size of the
universe is large as it will be very difficult to
prepare sampling frame.

33. (iii) Cluster Sampling
● This method is used when the size of population is
very large.
● The universe is divided into some clusters from
which sampling is carried out in a number of
stages.
● This method is used when we need to divide and
subdivide the population on the basis of certain
characteristics.
● For example, if we need to conduct a survey in a
country, we will first divide a country into
regions or states (stage I), then into cities or
towns (stage II) then further into localities (stage
III) etc. At each stage sampling is done by a
suitable method (say simple random sampling).

35. Merits
(1) Covers large area- This method is useful
when large area is to be studied as sampling is
done through various stages.
(2) Flexible- It is a flexible method as it enables
existing divisions and further subdivisions to be
used as samples at various stages.
Demerits
(1) Expensive- Since sampling is done at various
stages, this is expensive in terms of time, money
and efforts.
(2) Less accurate- It is generally less accurate as
compared to a method in which a sample has been
selected by some suitable single stage process.

36. II. Non Probability Sampling Methods
(i) Purposive/Deliberate/Judgement Sampling
● Purposive sampling is that method in which the
investigator himself makes the choice of the
sample items which in his opinion are the best
representative of the universe.
● Thus, in this method of sampling, selection of
the sample items is not left to the chance factors;
it is simply made by choice.

37. ● This method of sampling is specifically suitable
when some of the items in the universe are of
special significance and ought to be included in
the sample.
● However, there is a considerable possibility of
personal bias in purposive sampling. As a result, it
loses its credibility.

38. Merits
(1) Flexible- Since purposive sampling allows
inclusion of significant items in the sample, this
method is flexible in use.
(2) Facilitates purpose of study- Selection of
items for the sample can be done deliberately to
suit the objective of study.
(3) Simple- This method ensures simplicity in
the process of sample selection as it is based on
opinion of the investigator.

39. Demerits
(1) Biased- This method suffers from personal
bias of the investigator while selecting items
from the universe as it is left to the choice
factor.
(2) Not reliable- Since this method suffers
from personal bias of the investigator, the
samples thus selected may not be reliable.
(3) Inaccurate- This method gives inaccurate
results as samples depend on the whims of the
investigator. If the investigator is not
competent enough, one may get inaccurate
results.

40. (ii) Quota Sampling
● Method in which population is divided into
different groups or classes according to
different characteristics of the population,
is called Quota Sampling.
● The quota of the units to be observed by
the investigator is fixed in advance,
according to specified characteristics like
gender, age, annual income etc.
● This method is a mixture of stratified
sampling and deliberate sampling.

42. Merits
(1) Economical- This method of sampling is less
expensive. The cost of sampling and field work is
very low.
(2) Reliable- The results obtained are reliable
and dependable if the investigators involved are
skilled, experienced and competent.
Demerits
(1) Personal bias- There is a possibility of
personal prejudice at the time of selection of items.
(2) Impossible to detect sample error- It is
impossible to detect sampling error if the size of the
universe is large.

43. (iii) Convenience Sampling
● Method in which sampling is done by the
investigator in a manner that is according to his
convenience, is called Convenience Sampling.
● It is the simplest method as it serves the
purpose of convenience of the investigator.

44. Merits
(1) Simple- Since this method is based on the
discretion of the investigator, it is simple to execute.
(2) Inexpensive- This method is least expensive and
does not involve huge costs.
Demerits
(1) Unreliable- Since this method is based on the
discretion of the investigator, the results so obtained
can be unrealiable.
(2) Unscientific- This method is unscientific in nature
as it is based on whims and fancies of the investigator.
(3) Personal bias- Convenience samples are prone to
personal bias of the investigator.

45. Essentials of a Good Sample
(1) Representative: A sample must represent all
the characteristics of the universe. It is
possible only when each unit of the universe
stands equal chances of being selected in the
sample.
(2) Independent: Selection of one item of the
universe in the sample should not depend on
selection of some other item in the sample. All
items in the population should be independent of
each other.

46. (3) Homogeneity: If more than one sample are
selected from a universe, these samples should
be homogeneous (and not contradictory) to each
other.
(4)Adequacy/Sufficiency: The number of items
in the sample should be fairly adequate so that
some reliable conclusions are drawn covering
the characteristics of the universe as a whole.

47. Reliability of Sampling Data
(1) Size of the Sample: Reliability of sampling
depends on the size of the sample. If its size is very
small, it will fail to represent the population.
Accordingly, the conclusions would lack reliability.
(2) Method of Sampling: If the method of
sampling is not simple and exhaustive, it will not
adequately represent the Population.
(3) Bias of Correspondents and Enumerators:
Personal bias of the correspondents and
enumerators should be as less as possible.
Otherwise, reliability of the sampling data is
bound to suffer.

48. (4) Training of Enumerators: Reliability of
sample also depends upon the training of the
investigators. If they are not trained to make
them expert in their field of investigation, the
sample will lack reliability.

49. Statistical Errors
● In statistical terms, the difference between
the collected of data and actual value of facts
is termed as statistical errors.
● In other words, the difference between
estimated value and the actual value is called
statistical error.
Causes of Statistical Errors
● Selection of inadequate samples.
● Selection of wrong samples.
● Personal biasness of the investigator.
● Wrong information given by informants.
● Delay of information specially while depending on
local sources or correspondents.

50. Types of Statistical Errors
(a) Sampling Errors – It is the error which arises
due to drawing inferences about the universe or
population on the basis on a smaller sample.
● It is possible to reduce the magnitude of sampling
error by taking a larger sample.
For example: Consider a case of incomes of 5 farmers
in Manipur. Their incomes are Rs.500, 550, 600, 650
and 700. The average income would be Rs.600.
Suppose we select a sample of two persons out of 5 as
500 and 600. The average income now would be (500 +
600) ÷ 2 = Rs.550
Here the sampling error is Rs.600 (true value) —
Rs.550 (estimated value) = Rs.50

51. (b) Non – Sampling Errors – The errors which
arise at the stages of ascertainment and analysis
of data are called non sampling errors.
● These are more serious than sampling errors
because where sampling errors can be minimized
by taking a larger sample, non-sampling errors
can not be minimized even by taking a larger
sample.
● Even census can contain non-sampling errors.
● Some of the non sampling errors are:-
(i) Errors in data acquisition.
(ii) Non response error
(iii) Lack of trained investigators

53. Presented by –
Ritvik Tolumbia
CS, CWA, M.Com (ABST), M.A (Eco), B.Ed