This document discusses population and sampling concepts in statistics. It defines a population as the total collection of objects under study, while a sample is a subset of a population that is used to make inferences about the whole. Some key points made: - Populations can be finite or infinite in size and existent or hypothetical. - Samples are used when populations are too large to study entirely. Common sampling methods include simple random sampling, cluster sampling, and systematic sampling. - Non-probability sampling includes convenience sampling, snowball sampling, and quota sampling.

1. Savitribai Phule Pune University, Pune
FYBSc (CS)
Paper – II : Continuous Probability Distribution and Testing of Hypothesis (CPDTH)
TOPIC- POPULATION AND SAMPLE
By,
Prof. Shriram Kargaonkar
Asst. Prof. & HOD, Department of Statistics,
NSS Program Officer and Unnat Bharat Abhiyan Coordinator,
MAEER’s MITACSC Alandi, Pune- 412105
Email – snkargaonkar@mitacsc.ac.in
Mobile- 9762003712

2. Introduction
• In Statistics, data plays an essential role in
deciding the validity of the outcome.
• The data being used must be relevant, correct,
and representative of all classes.
• While more data is good to get impartial
results, it is crucial to make sure that the data
collected is suitable for the problem at hand.
• In this lecture, the concept of Population and
Sample will be explained in the simplest way.

3. Population
The totality of all objects under study.
The Collection of all objects under study.
Objects can be can be a group of individuals, a
set of items, etc.
It makes up the data pool for a study.

4. Population Examples
1) Number of students appearing for the FYBSc (CS) exam.
2) Total number of Students appearing for a particular exam in a particular
city, district, state or country.
3) Total number of people in the country.
4) Total number of items manufactured by the company.
5) Total number of diabetic patients in the city.
6) Number of stars in the sky
7) Number of leaves on the tree
8) Total blood in the body
9) Number of students in the class.
10) Number of industries/companies/business in a particular region.

5. Types of Population
There are different types of population. They are:
Finite Population: Countable / Finite number of elements
Infinite Population: Uncountable / infinite number of elements.
Existent Population: population of concrete individuals/ available in solid
form
Hypothetical Population: whose unit is not available in solid form

6. Sample
It is the representative part of the population.
A sample refers to a smaller, manageable version of a larger group.
It is a subset containing the characteristics of a larger population.
Samples are used in statistical testing when population sizes are too
large for the test to include all possible members or observations.
In other words, it is a portion, part, or fraction of the whole group,
and acts as a subset of the population.
Sample Examples
1) Selecting a handful of grains to check the quality of the grain to make decision of
purchasing or nor.
2) To check the blood group, just few drops are taken instead of whole blood.
3) To select appropriate number of diabetic patients among many to conduct a research
based on them.
4) To select few students among entire class for question answer session during the class.
5) Selecting 10 digits randomly out of 1 to 100.
6) Selecting few items among all the manufactured items to decide the quality of the
product etc.

8. Case Studies to understand the “sample”
1) Use of Social Media among youths
2) Opinion about politics in Maharashtra.
3) Financial Awareness among people in rural
area.
4) Opinion of students regarding mode of
examination.
5) Mode of transport of students
6) Opinion of preference of mobile phone
brands among people etc....

9. Types of Sampling

12. Types of Simple Random Sampling (SRS)
Simple Random Sampling With
Replacement (SRSWR)
Simple Random Sampling Without
Replacement (SRSWOR)
 Items selected at every draw, is
replaced back in the population
 If there are ‘N’ items in the
population then at every draw,
every item has the equal chance of
being selected in the sample i.e.
1/N
 Items selected at every draw, is not
replaced back in the population and
it is kept aside.
 If there are ‘N’ items in the
population then at every draw,
probability of getting selected
changes i.e. 1/N, 1/(N-1) , ....etc.

14. Cluster Sampling
It is a method where the researchers divide the entire
population into sections or clusters that represent a
population.
It Contains heterogeneous population.
Clusters are identified and included in a sample based
on demographic parameters like age, sex, location, etc.
This makes it very simple for a survey creator to derive
effective inference from the feedback.

15. Systematic Sampling Method
 Researchers use the Systematic Sampling Method to
choose the sample members of a population at regular
intervals.
 It requires the selection of a starting point for the sample
and sample size that can be repeated at regular intervals.
 This type of sampling method has a predefined range, and
hence this sampling technique is the least time-consuming.

17. Types of Non-Probability Sampling
1) Convenience Sampling. The selection of these cases is due to the
accessibility of the inclusion of the element and the proximity of this
subject with the researcher. It is useful when it is necessary to have
information quickly and inexpensively, regardless of whether it is
generalizable to the population. When a person approaches us in the
street to fill out a survey, it is convenience sampling.
2) Snowball Sampling. Snowball sampling — also known as referral sampling
— is carried out on populations in which their individuals are not known,
or it is tough to access them. So each subject studied proposes others, in
such a way that generates a cumulative effect of observations. It is widely
used in public policy and social studies. This is the most common system
for finding information on organized crime.
3) Quota Sampling. Quota sampling is based on selecting the sample after
dividing the population into strata. The subjects within each group are
chosen by non-probabilistic methods. Furthermore, the number of
elements selected is due to an arbitrary number (quotas) from which a
sample relatively proportional to the population is built.