Statistics and its application

Definition
A branch of mathematics dealing with the
• Collection,
• Analysis,
• Interpretation and
• Presentation of masses of numerical data.
A collection of quantitative data. Medical statistics
or biostatistics can be called quantitative medicine

Common Statistical Terms
Variable:
• A characteristic that takes on different values in
different persons, places or things.
• A quantity that varies within limits such as height,
weight, blood pressure, age, etc.
• It is denoted as X and notation for orderly series
as X1, X2, X3, ….Xn.
• The suffix n is symbol for number in the series.
• Σ (sigma) stands for summation or results or
observation.

Constant:
Quantities that do not vary
such as π = 3.1416, e = 2.7183.
They do not require statistical study.
In biostatistics, mean, standard deviation,
standard error, correlation coefficient and
proportion of a particular population are
considered as constant.

Observation:
• An event and its measurements
such as
• blood pressure (event)
• 120 mmHg (measurement).
• Observational unit: The source that gives
observations such as object, person, etc.

Data:
A set of values recorded
on one or more observational units.
Data are raw materials of statistics.

Population:
It is an entire group of people or study
elements—persons, things or measurements for
which we have an interest at a particular time.
infinite or finite
• If a population consists of fixed number of
values, it is said to be finite.
• If population consists of an endless succession
of values. The population is an infinite one.

• Sampling unit: Each member of a population.
• Sample: It may be defined as a part of a
population. It is a group of sampling units that
form part of a population.

Parametric test:
It is one in which population constants as
described above are used such as mean,
variances, etc. and data tend to follow one
assumed or established distribution such as
normal, binomial, Poisson, etc.

Nonparametric tests:
Tests such as χ2 test, in which no constant of a
population is used. Data do not follow any
specific distribution and no assumptions are
made in nonparametric tests, e.g. to classify
good, better and best you allocate arbitrary
numbers or marks to each category

Notations for a Population and
Sample Values
Roman letters are used for statistics of samples and
Greek for parameters of population.
sample Population
• Mean X μ
• Standard deviation s s
• Variance s2 σ2
• Proportion p P or π
• Proportion Complement of q Q or (1– π)

Other symbols commonly used are:
= : Equal to
> : Greater than
> : Greater than or equal to
< : Less than
< : Less than or equal to
Z : The number of standard deviations from the
mean
or standard normal deviate/variate
% : Percent

Other symbols commonly used are:
r : Pearson’s correlation coefficient
p : Spearman’s correlation coefficient
O : Observed number
E : Expected number
d.f. or df : Degrees of freedom
k : Number of groups or classes
P (A) : Probability of event A

A medical student should not depend on a
statistician for the statistical analysis.
He or she should take the guidance of a
qualified statistician right from the beginning of
any scientific study till drawing the conclusions.

Scope of statistics
• Planning
• Economics
• Business
• Industry
• Mathematics
• Modern science
• Psychology
• Education
• War
• Bank
• Astronomy
• Sociology

Scope of statistics In
Planning:
The government are planning for economic
development.
Economics:
It is useful in solving economical problem. Such as
wages, price, time series analysis, demand analysis.
Business:
Business executive are relying more and more on
statistical techniques for studying the much and
desire of the valued customers.

Industry:
Statistic tools such as inspection plan, control chart etc. used
in quality control to find out whether the product is
confirming to the specifications or not.
Mathematics:
statistical technique are the outcome of wide applications of
mathematics.
Modern science:
In medical science the statistical tools for collection,
presentation and analysis of observed facts relating to causes
and incidence of diseases and the result of application various
drugs and medicine are of great importance.

psychology and education:
In education and psychology statistics has found wide application such
as, determining or to determine the reliability and validity to a test,
factor analysis etc.
In war: The theory of decision function can be a great assistance to the
military and personal to plan “maximum destruction with minimum
effort.”
In banking:
it play an important role in banking. The banks make use of statistics
for a number of purposes. The banks work on the principle that all the
people who deposit their money with the banks do not withdraw it at
the same time. The bankers use statistical approaches based on
probability to estimate the numbers of depositors and their claims for
a certain day.

In State Management (Administration):
Statistics is essential for a country.
it helps in estimating the expected expenditures and
revenue from different sources.
So statistics are the eyes of administration of the state.
In Accounting and Auditing: accounting is impossible
without exactness. The correction of the values of current
asserts is made on the basis of the purchasing power of
money or the current value of it. In auditing sampling
techniques are commonly used. An auditor determines
the sample size of the book to be audited on the basis of
error.

In Natural and Social Sciences:
Statistical methods are commonly used for analyzing the experiments
results, testing their significance in Biology, Physics, Chemistry,
Mathematics, Meteorology, Research chambers of commerce,
Sociology, Business, Public Administration, Communication and
Information Technology etc
In Astronomy:
Astronomy is one of the oldest branches of statistical study; it deals
with the measurement of distance, sizes, masses and densities of
heavenly bodies by means of observations. During these
measurements errors are unavoidable so most probable
measurements are founded by using statistical methods.
Sociology:
The sociologist may be called upon for help with a special problem
such as social conflict, urban plight or the war on poverty or crimes.

Government:
The functions of a government are more varied and
complex.
Various departments in the state are required to
collect and record statistical data in a systematic
manner for an effective administration.
Data pertaining to various fields namely population,
natural resources, production both agricultural and
industrial, finance, trade, exports and imports etc
are the most fundamental requirements of the
state for its administration.

Functions of statistics
• Without a statistical study, our ideas would be
vague and indefinite.
• statistics helps in simplifying complex data to
simple-to make them understandable.
• To test a new theory.
• It help in shaping future policies.
• To draw a rational conclusion

Advantages of statistics
• Analyzed relatively quickly
• Information is collected in a standardized way.
• It is required and respected by decision-
makers.
• It can be used to collect wide range of
information.

Disadvantages of statistics
• It is not appropriate to understand the issues
in great depth.
• They are not suitable to evaluate user
opinions.
• It may be time-consuming to arrange
methods of data collection.
• The risk of accidentally choosing very common
cases is more apparent in standardised
pattern of population.

• There is a greater risk of data manipulation.
• it is a delicate science and can be easily
misused by an unscrupulous person.
• Statistical cannot be applied to heterogeneous
data.
• It sufficient care is not exercised in collecting,
analyzing and interpretation the data,
statistical results might be misleading.
Disadvantages of statistics

Statistics and its application

Recommended

More Related Content

What's hot (20)

Similar to Statistics and its application (20)

More from gopinathannsriramachandraeduin (20)

Recently uploaded (20)

Statistics and its application