Welcome to Ctanujit Institute of Statistics & Mathematics...An Initiative by 'ISI'ian

An Introduction to Statistics-What is Statistics?

CONTENT:

Definition,explanation of terms,difficulties,career opportunities
"Status"-"State"->"Statistics".



STEPS AT A GLANCE :
Collection of Data-> Summarisation of Data-> Analysis of Data-> Interpretation of Data towards a VALID DECISION.

WHAT IS THE MAIN PROBLEM IN STATISTICS?
Given a sample(a set of outcomes),we are to say(infer) about the population or the model.Statistics primarily deals with situations in which the occurrence of some event can't. be predicted with certainty.

WHAT ARE THE MAJOR OBJECTIVES OF STATISTICS?
1. To make inference about a population from an analysis of information contained in the sample data.
2. To make assessments of the extent of uncertainty involved in these inferences.
A third objective,no less important,is to design the process & the extent of sampling so that the observations from a basis for drawing valid & accurate inferences.

GIVE THE DEFINITION OF STATISTICS?
"STATISTICS" is a science of decision making on the basis of sample observations drawn from a population under uncertainty. That is, it is a mathematical discipline concerned with collection of data,summarisation of data,analysis of data & interpretation of data toward a valid decision.
Encyclopaedia Americana :-
As a name of a field of study, Statistics refers to the science & arts of obtaining & analysing quantitative data with a view to make sound inferences in the face of uncertainty.
Encyclopaedia Britannica:-
As is commonly understood now a days, Statistics is a mathematical discipline concerned with the study of masses of quantitative data of any kind.

WHAT IS THE MEANING OF THE TERM 'STATISTICS'?
As a singular noun it refers the science of collecting,analysing & interpreting numerical data relating to an aggregate of individuals. As a plural noun it denotes the numerical & quantitative information,e.g., labour statistics,vital statistics.

IS STATISTICS A SCIENCE?
Any Science has for its objectives the formulation of laws for explaining phenomena in some part of the real world with a deterministic view-point.
As Kendall explained ," Statistics is the branch of scientific method which deals with the data obtained by counting or measuring the properties of population of natural phenomena".
Indeed, we can call Statistical Methodology as Scientific Method. It is noted that STATISTICS is sometimes called the study of variation, i.e., a population or group without any variation & uncertainty is no interest to Statistics. So, Statistics is the scientific methodology which deals with the collection,classification & tabulation of numerical facts as a basis for explanation,description & comparison of social phenomena.

DEFINE THE TERMS: STATISTICAL DATA,POPULATION,SAMPLE.
Statistical Data:- The numerical data or measurements obtained in case of an enquiry into a phenomenon,marked by uncertainty & variability,constitute Statistical Data. Uncertainty & variability are two major characteristics of Statistical data. Not all quantitative data is statistical data. Example of statistical data--Suppose we study the 'Heights of students in a particular college'.Here we can't predict the height of an individual with certainty & there will be variation in heights of students. Counter Example:--Multiplication table in a tabular form is a quantitative data,but since there is no uncertainty & variability involved in the data so it's not a Statistical Data.
Population:- A set or group of observations relating to a phenomenon under statistical investigation is known as statistical population or simply population. However,the term 'population' implies an aggregate or collection of measurements on a given variable(s). Population is said to be finite or infinite according to whether the set contains a finite or infinite number of observations.
Example-Measurements of heights in your college.
Note that: I. The characteristics of a population are called parameters. II.A population contains finite or infinite no of observations on a given variable(s).
Sample :- The set of data actually collected through a process of observation from selected items of any source is called a Sample. However, "Sample" is a subset of population or a true representation of population.
Example- Measurements of heights of students of Statistics department in your college.
Note that:- I. The characteristics of sample are called as Statistic. II. A sample is taken in order to gather information about a population.

WRITE DOWN THE DRAWBACKS OF STATISTICS?
Limitations of Statistics: I. Statistics deals with quantitative data only. II. Statistical law holds good only for aggregate of items or average individuals. It may not true for a particular individual or item. III. Inadequate knowledge of data interpretation may lead to invalid decision.
There are some sayings: "There are there kinds of lies--lies,white lies & Statistics" , "Figure won't lie,but liars figure" , "Statistics is like a clay of which you can make a god or a devil".

COMMENT ON THE FOLLOWING: "In a study of ages & professions of deceased men, it was found that the profession with the lowest average age of death was 'student' .So it appears that student profession is very dangerous."
It is obvious that every professional must have some basic education & it happens that the average age of every professional men must be higher than the age of the students. But it can happen that profession with lowest age of death was student . So the given statement is TRUE. But the conclusion made from the fact is incorrect . It can never be told that the student profession is dangerous. To conclude properly,we must have data for computing the proportions or percentages of deceased men in different professions. Therefore the conclusion made here is absurd.
This is an example of the situation where inadequate information takes into bad decisions. Statistics is a science of DECISION MAKING. So,wrong data interpretation will show some absurd decision,might be harmful for society.

EXPLAIN THE STATEMENT : "Blindly using any data happened to be available can lead to misleading information & bad decision."
There are two kinds of people: Some of them believe that the inferences based on statistical data are very reliable & trusty. And others don't believe statistical results at all,they think it as a damned lies. But the fact is statistics is sometimes misused either deliberately or often due to lack of knowledge. Making conclusions based on inadequate information,deliberate manipulation & personal bias may lead to bad decision. Statistics are not to be blamed for all these. Statistical methods are most danger tool in the hand of non-experts.Lastly Statistics is like a clay of which you can make a god or a devil.