This document discusses populations and samples in statistics. It defines a population as the entire group being studied, while a sample is a subset of the population. Taking a sample is necessary because it is usually impossible or impractical to study every individual in a population due to constraints of time, resources, and accessibility. Parameters describe characteristics of the entire population, while statistics describe characteristics of a sample. Inferential statistics allows making educated guesses about population parameters based on sample statistics. An example is given of a denim manufacturer examining a sample of jeans to draw conclusions about the quality of stitching in the entire production population.

1. Presented by
Dr. R. RAJA, M.E., Ph.D.,
Assistant Professor, Department of EEE,
Muthayammal Engineering College, (Autonomous)
Namakkal (Dt), Rasipuram – 637408
Population and Sample in Total Quality Management
MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC, NBA & Affiliated to Anna University),
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu.

2. Population and Sample
What Is Population?
 In statistics, a population is the entire pool from which a statistical sample is
drawn. A population may refer to an entire group of people, objects, events,
hospital visits, or measurements.
 A population can thus be said to be an aggregate observation of subjects
grouped together by a common feature.
 Unlike a sample, when carrying out statistical analysis on a population, there
are no standard errors to report that is, because such errors inform analysts
using a sample how far their estimate may deviate from the true population
value. But since you are working with the true population you already know the
true value.
11/11/2020 2

3. Count..
The Basics of Population
 A population can be defined by any number of characteristics within a group that
statisticians use to draw conclusions about the subjects in a study. A population
can be vague or specific. Examples of population (defined vaguely) include the
number of newborn babies in North America, total number of tech startups in
Asia, average height of all CFA exam candidates in the world, mean weight of
U.S. taxpayers and so on.
 Population can also be defined more specifically, such as the number of newborn
babies in North America with brown eyes, the number of startups in Asia that
failed in less than three years, the average height of all female CFA exam
candidates, mean weight of all U.S. taxpayers over 30 years of age, among others.
11/11/2020 3

4. Count..
 Most times, statisticians and researchers want to know the characteristics of
every entity in a population, so as to draw the most precise conclusion possible.
This is impossible or impractical most times, however, since population sets
tend to be quite large.
 For example, if a company wanted to know whether each of its 50,000
customers serviced during the year was satisfied, it might be challenging,
costly and impractical to call each of the clients on the phone to conduct
a survey. Since the characteristics of every individual in a population cannot be
measured due to constraints of time, resources, and accessibility, a sample of
the population is taken.
11/11/2020 4

5. Count..
Population Samples
 A sample is a random selection of members of a population.
 It is a smaller group drawn from the population that has the characteristics of
the entire population.
 The observations and conclusions made against the sample data are attributed to
the population.
 The information obtained from the statistical sample allows statisticians to
develop hypotheses about the larger population.
 In statistical equations, population is usually denoted with an uppercase N while
the sample is usually denoted with a lowercase n.
11/11/2020 5

6. Count..
Population Parameters
 A parameter is data based on an entire population. Statistics such as averages
and standard deviations, when taken from populations, are referred to as
population parameters.
 The population mean and population standard deviation are represented by the
Greek letters µ and σ, respectively.
 The standard deviation is the variation in the population inferred from the
variation in the sample.
 When the standard deviation is divided by the square root of the number of
observations in the sample, the result is referred to as the standard error of the
mean.
11/11/2020 6

7. Count..
 While a parameter is a characteristic of a population, a statistic is a
characteristic of a sample.
 Inferential statistics enables you to make an educated guess about a population
parameter based on a statistic computed from a sample randomly drawn from
that population.
11/11/2020 7

8. Count..
Real World Example of Population
 For example, let's say a denim apparel manufacturer wants to check the quality
of the stitching on its blue jeans before shipping them off to retail stores.
 It is not cost effective to examine every single pair of blue jeans the
manufacturer produces (the population).
 Instead, the manufacturer looks at just 50 pairs (a sample) to draw a conclusion
about whether the entire population is likely to have been stitched correctly.
11/11/2020 8

9. Thank You
11/11/2020 9